Latest in math.st

total 9324took 0.44s
Parametric inference for multidimensional hypoelliptic diffusion with full observationsFeb 08 2018Multidimensional hypoelliptic diffusions arise naturally as models of neuronal activity. Estimation in those models is complex because of the degenerate structure of the diffusion coefficient. We build a consistent estimator of the drift and variance ... More
Gradient conjugate priors and deep neural networksFeb 07 2018The paper deals with learning the probability distribution of the observed data by artificial neural networks. We suggest a so-called gradient conjugate prior (GCP) update appropriate for neural networks, which is a modification of the classical Bayesian ... More
Sparse Linear Discriminant Analysis under the Neyman-Pearson ParadigmFeb 07 2018In contrast to the classical binary classification paradigm that minimizes the overall classification error, the Neyman-Pearson (NP) paradigm seeks classifiers with a minimal type II error while having a constrained type I error under a user-specified ... More
Group kernels for Gaussian process metamodels with categorical inputsFeb 07 2018Gaussian processes (GP) are widely used as a metamodel for emulating time-consuming computer codes.We focus on problems involving categorical inputs, with a potentially large number L of levels (typically several tens),partitioned in G << L groups of ... More
Wishart laws and variance function on homogeneous conesFeb 07 2018We present a systematic study of Riesz measures and their natural exponential families of Wishart laws on a homogeneous cone. In the non-singular case, we compute explicitly the inverse of the mean map and the variance function of a Wishart exponential ... More
Splitting models for multivariate count dataFeb 06 2018Considering discrete models, the univariate framework has been studied in depth compared to the multivariate one. This paper first proposes two criteria to define a sensu stricto multivariate discrete distribution. It then introduces the class of splitting ... More
The nonparametric LAN expansion for discretely observed diffusionsFeb 06 2018Consider a scalar reflected diffusion $(X_t)_{t\geq 0}$, where the unknown drift function $b$ is modelled nonparametrically. We show that in the low frequency sampling case, when the sample consists of $(X_0,X_\Delta,...,X_{n\Delta})$ for some fixed sampling ... More
Quantifying dependencies for sensitivity analysis with multivariate input sample dataFeb 06 2018We present a novel method for quantifying dependencies in multivariate datasets, based on estimating the R\'{e}nyi entropy by minimum spanning trees (MSTs). The length of the MSTs can be used to order pairs of variables from strongly to weakly dependent, ... More
Dynamic Spatial Panel Models: Networks, Common Shocks, and Sequential ExogeneityFeb 06 2018This paper considers a class of GMM estimators for general dynamic panel models, allowing for weakly exogenous covariates and cross sectional dependence due to spatial lags, unspecified common shocks and time-varying interactive effects. We significantly ... More
On singular value distribution of large dimensional data matrices whose columns have different correlationsFeb 05 2018Suppose $\mathbf Y_n=(\mathbf y_1,\cdots,\mathbf y_n)$ is a $p\times n$ data matrix whose columns $\mathbf y_j, 1\leq j\leq n$ have different correlations. The asymptotic spectral property of $\mathbf S_n=\frac1n\mathbf Y_n\mathbf Y^*_n$ when $p$ increase ... More
Distance Metrics for Gamma DistributionsFeb 03 2018Here I present the analytic form of two common distance metrics, the symmetrised Kullback-Leibler Divergence and the Kolmogorov-Smirnov statistic, as well as an extension of the Kolmogorov-Smirnov statistic for comparing theoretical gamma distributions. ... More
On the Minimax Misclassification Ratio of Hypergraph Community DetectionFeb 03 2018Community detection in hypergraphs is explored. Under a generative hypergraph model called "d-wise hypergraph stochastic block model" (d-hSBM) which naturally extends the Stochastic Block Model from graphs to d-uniform hypergraphs, the asymptotic minimax ... More
De-biased sparse PCA: Inference and testing for eigenstructure of large covariance matricesJan 31 2018Sparse principal component analysis (sPCA) has become one of the most widely used techniques for dimensionality reduction in high-dimensional datasets. The main challenge underlying sPCA is to estimate the first vector of loadings of the population covariance ... More
Noise contrastive estimation: asymptotics, comparison with MC-MLEJan 31 2018A statistical model is said to be un-normalised when its likelihood function involves an intractable normalising constant. Two popular methods for parameter inference for these models are MC-MLE (Monte Carlo maximum likelihood estimation), and NCE (noise ... More
Comparison of robustness of statistical procedures for network structure analysisJan 30 2018Different network structures are compiared with respect to degree of robustnes of identification statistical procedures. It is shown that threshold (market) graph, cliques and independent sets in the threshold (market) graphs are preferable network structure ... More
Mixture Proportion Estimation for Positive--Unlabeled Learning via Classifier Dimension ReductionJan 30 2018Jan 31 2018Positive--unlabeled (PU) learning considers two samples, a positive set $P$ with observations from only one class and an unlabeled set $U$ with observations from two classes. The goal is to classify observations in $U$. Class mixture proportion estimation ... More
Adaptive Estimation of Noise Variance and Matrix Estimation via USVT AlgorithmJan 28 2018Consider the problem of denoising a large $m\times n$ matrix. This problem has received widespread attention in recent years. A common approach is to assume that the denoised matrix is of low rank and then apply a thresholding algorithm. The error bound ... More
Generalized Estimating Equation for the Student-t DistributionsJan 27 2018In \cite{KumarS15J2}, it was shown that a generalized maximum likelihood estimation problem on a (canonical) $\alpha$-power-law model ($\mathbb{M}^{(\alpha)}$-family) can be solved by solving a system of linear equations. This was due to an orthogonality ... More
Strong-consistent autoregressive predictors in abstract Banach spacesJan 26 2018This work derives new results on the strong-consistency of a componentwise estimator of the autocorrelation operator, and its associated plug-in predictor, in the context of autoregressive processes of order one, in a real separable Banach space $B$ (ARB(1) ... More
Concentration of random graphs and application to community detectionJan 26 2018Random matrix theory has played an important role in recent work on statistical network analysis. In this paper, we review recent results on regimes of concentration of random graphs around their expectation, showing that dense graphs concentrate and ... More
Concentration without measureJan 26 2018Although there doesn't exist the Lebesgue measure in the ball $M$ of $C[0,1]$ with $p-$norm, the average values (expectation) $EY$ and variance $DY$ of some functionals $Y$ on $M$ can still be defined through the procedure of limitation from finite dimension ... More
On all Pickands Dependence Functions whose corresponding Extreme-Value-Copulas have Spearman $ρ$ (Kendall $τ$) identical to some value $v \in [0,1]$Jan 23 2018We answer an open question posed by the second author at the Salzburg workshop on Dependence Models and Copulas in 2016 concerning the size of the family $\mathcal{A}^\rho_v$ ($\mathcal{A}^\tau_v$) of all Pickands dependence functions $A$ whose corresponding ... More
Propensity score methodology in the presence of network entanglement between treatmentsJan 22 2018In experimental design and causal inference, it may happen that the treatment is not defined on individual experimental units, but rather on pairs or, more generally, on groups of units. For example, teachers may choose pairs of students who do not know ... More
Limiting Distributions of Spectral Radii for Product of Matrices from the Spherical EnsembleJan 21 2018Consider the product of $m$ independent $n\times n$ random matrices from the spherical ensemble for $m\ge 1$. The spectral radius is defined as the maximum absolute value of the $n$ eigenvalues of the product matrix. When $m=1$, the limiting distribution ... More
Joint CLT for eigenvalue statistics from several dependent large dimensional sample covariance matrices with applicationJan 20 2018Let $\mathbf{X}_n=(x_{ij})$ be a $k \times n$ data matrix with complex-valued, independent and standardized entries satisfying a Lindeberg-type moment condition. We consider simultaneously $R$ sample covariance matrices $\mathbf{B}_{nr}=\frac1n \mathbf{Q}_r ... More
A Precise Analysis of PhaseMax in Phase RetrievalJan 20 2018Recovering an unknown complex signal from the magnitude of linear combinations of the signal is referred to as phase retrieval. We present an exact performance analysis of a recently proposed convex-optimization-formulation for this problem, known as ... More
Joint estimation of parameters in Ising modelJan 19 2018We study joint estimation of the inverse temperature and magnetization parameters $(\beta,B)$ of an Ising model with a non-negative coupling matrix $A_n$ of size $n\times n$, given one sample from the Ising model. We give a general bound on the rate of ... More
Minimax Optimal Additive Functional Estimation with Discrete Distribution: Slow Divergence Speed CaseJan 12 2018This paper addresses an estimation problem of an additive functional of $\phi$, which is defined as $\theta(P;\phi)=\sum_{i=1}^k\phi(p_i)$, given $n$ i.i.d. random samples drawn from a discrete distribution $P=(p_1,...,p_k)$ with alphabet size $k$. We ... More
Shapley effects for sensitivity analysis with dependent inputs: bootstrap and kriging-based algorithmsJan 10 2018In global sensitivity analysis, the well known Sobol' sensitivity indices aim to quantify how the variance in the output of a mathematical model can be apportioned to the different variances of its input random variables. These indices are based on the ... More
On the consistency of adaptive multiple testsJan 08 2018Much effort has been done to control the "false discovery rate" (FDR) when $m$ hypotheses are tested simultaneously. The FDR is the expectation of the "false discovery proportion" $\text{FDP}=V/R$ given by the ratio of the number of false rejections $V$ ... More
Finite-sample risk bounds for maximum likelihood estimation with arbitrary penaltiesDec 29 2017The MDL two-part coding $ \textit{index of resolvability} $ provides a finite-sample upper bound on the statistical risk of penalized likelihood estimators over countable models. However, the bound does not apply to unpenalized maximum likelihood estimation ... More
Estimation for high-frequency data under parametric market microstructure noiseDec 05 2017In this paper, we propose a general class of noise-robust estimators based on the existing estimators in the non-noisy high-frequency data literature. The market microstructure noise is a known parametric function of the limit order book. The noise-robust ... More
Ranking Median Regression: Learning to Order through Local ConsensusOct 31 2017Dec 18 2017This article is devoted to the problem of predicting the value taken by a random permutation $\Sigma$, describing the preferences of an individual over a set of numbered items $\{1,\; \ldots,\; n\}$ say, based on the observation of an input/explanatory ... More
Quantifying the Estimation Error of Principal ComponentsOct 27 2017Principal component analysis is an important pattern recognition and dimensionality reduction tool in many applications. Principal components are computed as eigenvectors of a maximum likelihood covariance $\widehat{\Sigma}$ that approximates a population ... More
Optimal Rates for Learning with Nyström Stochastic Gradient MethodsOct 21 2017In the setting of nonparametric regression, we propose and study a combination of stochastic gradient methods with Nystr\"om subsampling, allowing multiple passes over the data and mini-batches. Generalization error bounds for the studied algorithm are ... More
Nonparametric estimation of multivariate distribution function for truncated and censored lifetime dataOct 20 2017In this article we consider a number of models for the statistical data generation in different areas of insurance, including life, pension and non-life insurance. Insurance statistics are usually truncated and censored, and often are multidimensional. ... More
The Geometry of GaussoidsOct 19 2017A gaussoid is a combinatorial structure that encodes independence in probability and statistics, just like matroids encode independence in linear algebra. The gaussoid axioms of Lnenicka and Mat\'us are equivalent to compatibility with certain quadratic ... More
Duality of Graphical Models and Tensor NetworksOct 04 2017In this article we show the duality between tensor networks and undirected graphical models with discrete variables. We study tensor networks on hypergraphs, which we call tensor hypernetworks. We show that the tensor hypernetwork on a hypergraph exactly ... More
Interpretable High-Dimensional Inference Via Score Projection with an Application in NeuroimagingSep 26 2017In the fields of neuroimaging and genetics, a key goal is testing the association of a single outcome with a very high-dimensional imaging or genetic variable. Often, summary measures of the high-dimensional variable are created to sequentially test and ... More
Estimating graph parameters via random walks with restartsSep 04 2017In this paper we discuss the problem of estimating graph parameters from a random walk with restarts at a fixed vertex $x$. For regular graphs $G$, one can estimate the number of vertices $n_G$ and the $\ell^2$ mixing time of $G$ from $x$ in $\widetilde{O}(\sqrt{n_G}\,(t_{\rm ... More
Isotonic regression in general dimensionsAug 30 2017We study the least squares regression function estimator over the class of real-valued functions on $[0,1]^d$ that are increasing in each coordinate. For uniformly bounded signals and with a fixed, cubic lattice design, we establish that the estimator ... More
A unified theory for exact stochastic modelling of univariate and multivariate processes with continuous, mixed type, or discrete marginal distributions and any correlation structureJul 21 2017Hydroclimatic processes are characterized by heterogeneous spatiotemporal correlation structures and marginal distributions that can be continuous, mixed-type, discrete or even binary. Simulating exactly such processes can greatly improve hydrological ... More
Generalization Properties of Doubly Online Learning AlgorithmsJul 03 2017Doubly online learning algorithms are scalable kernel methods that perform very well in practice. However, their generalization properties are not well understood and their analysis is challenging since the corresponding learning sequence may not be in ... More
Fast and General Model Selection using Data Depth and ResamplingJun 08 2017Nov 28 2017We present a technique using data depth functions and resampling to perform best subset variable selection for a wide range of statistical models. We do this by assigning a score, called an $e$-value, to a candidate model, and use a fast bootstrap method ... More
On the sample mean after a group sequential trialJun 05 2017Dec 18 2017A popular setting in medical statistics is a group sequential trial of maximal length $n$ with independent normal outcomes with mean $\mu$ and finite variance, in which interim analyses of the sum of the outcomes are performed at $0 < m_1 < \ldots < m_L ... More
Ancestral distributions in the coalescentMay 26 2017We consider inference about the history of a sample of DNA sequences, conditional upon the haplotype counts and the number of segregating sites observed at the present time. After deriving some theoretical results in the coalescent setting, we implement ... More
Discovery of statistical equivalence classes using computer algebraMay 26 2017Discrete statistical models supported on labelled event trees can be specified using so-called interpolating polynomials which are generalizations of generating functions. These admit a nested representation. A new algorithm exploits the primary decomposition ... More
On the Efficient Simulation of the Left-Tail of the Sum of Correlated Log-normal VariatesMay 22 2017May 26 2017The sum of Log-normal variates is encountered in many challenging applications such as in performance analysis of wireless communication systems and in financial engineering. Several approximation methods have been developed in the literature, the accuracy ... More
Thresholds For Detecting An Anomalous Path From Noisy EnvironmentsApr 20 2017We consider the "searching for a trail in a maze" composite hypothesis testing problem, in which one attempts to detect an anomalous directed path in a lattice 2D box of side n based on observations on the nodes of the box. Under the signal hypothesis, ... More
How to avoid the curse of dimensionality: scalability of particle filters with and without importance weightsMar 22 2017Sep 19 2017Particle filters are a popular and flexible class of numerical algorithms to solve a large class of nonlinear filtering problems. However, standard particle filters with importance weights have been shown to require a sample size that increases exponentially ... More
Spatial Adaptation in Trend FilteringFeb 16 2017We study trend filtering, a relatively recent method for univariate nonparametric regression. For a given integer $r \geq 1$, the trend filtering estimator of order $r$ is defined as the minimizer of the sum of squared errors when we constrain (or penalize) ... More
Asymptotic Independence of Bivariate Order StatisticsJan 31 2017It is well known that an extreme order statistic and a central order statistic (os) as well as an intermediate os and a central os from a sample of iid univariate random variables get asymptotically independent as the sample size increases. We extend ... More
Asymptotic and bootstrap tests for the dimension of the non-Gaussian subspaceJan 24 2017Dimension reduction is often a preliminary step in the analysis of large data sets. The so-called non-Gaussian component analysis searches for a projection onto the non-Gaussian part of the data, and it is then important to know the correct dimension ... More
Markov random fields and iterated toric fibre productsDec 20 2016Feb 07 2018We prove that iterated toric fibre products from a finite collection of toric varieties are defined by binomials of uniformly bounded degree. This implies that Markov random fields built up from a finite collection of finite graphs have uniformly bounded ... More
An asymptotic expansion for the normalizing constant of the Conway-Maxwell-Poisson distributionDec 20 2016Oct 16 2017The Conway-Maxwell-Poisson distribution is a two-parameter generalisation of the Poisson distribution that can be used to model data that is under- or over-dispersed relative to the Poisson distribution. The normalizing constant $Z(\lambda,\nu)$ is given ... More
Change point detection in heteroscedastic time seriesDec 08 2016Many time series exhibit changes both in level and in variability. Generally, it is more important to detect a change in the level, and changing or smoothly evolving variability can confound existing tests. This paper develops a framework for testing ... More
Minimum Rates of Approximate Sufficient StatisticsDec 08 2016Given a sufficient statistic for a parametric family of distributions, one can estimate the parameter without access to the data itself. However, the memory or code size for storing the sufficient statistic may nonetheless still be prohibitive. Indeed, ... More
Approximate Likelihood Construction for Rough Differential EquationsDec 08 2016The paper is split in two parts: in the first part, we construct the exact likelihood for a discretely observed rough differential equation, driven by a piecewise linear path. In the second part, we use this likelihood in order to construct an approximation ... More
Semi-Supervised linear regressionDec 07 2016We study a regression problem where for some part of the data we observe both the label variable ($Y$) and the predictors (${\bf X}$), while for other part of the data only the predictors are given. Such a problem arises, for example, when observations ... More
Nearly Random Designs with Greatly Improved BalanceDec 07 2016We present a new experimental design procedure that divides a set of experimental units into two groups so that the two groups are balanced on a prespecified set of covariates and being almost as random as complete randomization. Under complete randomization, ... More
Statistical and Computational Guarantees of Lloyd's Algorithm and its VariantsDec 07 2016Clustering is a fundamental problem in statistics and machine learning. Lloyd's algorithm, proposed in 1957, is still possibly the most widely used clustering algorithm in practice due to its simplicity and empirical performance. However, there has been ... More
Impossible Inference in Econometrics: Theory and Applications to Regression Discontinuity, Bunching, and Exogeneity TestsDec 06 2016This paper presents necessary and sufficient conditions for tests to have trivial power. By inverting these impractical tests, we demonstrate that the bounded confidence regions have error probability equal to one. This theoretical framework establishes ... More
A stochastic process approach to multilayer neutron detectorsDec 06 2016The sparsity of the isotope Helium-3, ongoing since 2009, has initi- ated a new generation of neutron detectors. One particularly promis- ing development line for detectors is multilayer gaseous detectors where the neutron conversion into charged ions ... More
Fiducial, confidence and objective Bayesian posterior distributions for a multidimensional parameterDec 06 2016We propose a way to construct fiducial distributions for a multidimensional parameter using a step-by-step conditional procedure related to the inferential importance of the components of the parameter. For discrete models, in which the non-uniqueness ... More
Necessary and Sufficient Condition for Asymptotic Standard Normality of the Two Sample PivotDec 06 2016The large sample solution to the problem of comparing the means of two populations with finite variances based on independent samples from the two populations relies on the pivotal quantity underpinning the construction of the confidence interval and ... More
Estimating Linear and Quadratic forms via Indirect ObservationsDec 05 2016In this paper, we further develop the approach, originating in [14 (arXiv:1311.6765),20 (arXiv:1604.02576)], to "computation-friendly" hypothesis testing and statistical estimation via Convex Programming. Specifically, we focus on estimating a linear ... More
Dynamic change-point detection using similarity networksDec 05 2016From a sequence of similarity networks, with edges representing certain similarity measures between nodes, we are interested in detecting a change-point which changes the statistical property of the networks. After the change, a subset of anomalous nodes ... More
Analysis of finite sample size quantum hypothesis testing via martingale concentration inequalitiesDec 05 2016Martingale concentration inequalities constitute a powerful mathematical tool in the analysis of problems in a wide variety of fields ranging from probability and statistics to information theory and machine learning. Here we apply such inequalities to ... More
On the regular conditional distribution of a multivariate Normal given a linear transformationDec 05 2016We show that the orthogonal projection operator onto the range of the adjoint of a linear operator T can be represented as UT, where U is an invertible linear operator. Using this representation we obtain a decomposition of a multivariate Normal random ... More
A note on the instability and degeneracy of deep learning modelsDec 04 2016A probability model exhibits instability if small changes in a data outcome result in large, and often unanticipated, changes in probability. For correlated data structures found in several application areas, there is increasing interest in predicting/identifying ... More
Algebraic Identifiability of Gaussian MixturesDec 04 2016We prove that all moment varieties of univariate Gaussian mixtures have the expected dimension. Our approach rests on intersection theory and Terracini's classification of defective surfaces. The analogous identifiability result is shown to be false for ... More
Algebraic Identifiability of Gaussian MixturesDec 04 2016Apr 04 2017We prove that all moment varieties of univariate Gaussian mixtures have the expected dimension. Our approach rests on intersection theory and Terracini's classification of defective surfaces. The analogous identifiability result is shown to be false for ... More
Change point detection in autoregressive models with no moment assumptionsDec 04 2016In this paper we consider the problem of detecting a change in the parameters of an autoregressive process, where the moments of the innovation process do not necessarily exist. An empirical likelihood ratio test for the existence of a change point is ... More
Stochastic Longshore Current DynamicsDec 04 2016We develop a stochastic parametrization, based on a `simple' deterministic model for the dynamics of steady longshore currents, that produces ensembles that are statistically consistent with field observations of these currents. Unlike deterministic models, ... More
Universal statistics of selected valuesDec 02 2016Selection, the tendency of some traits to become more frequent than others in a population under the influence of some (natural or artificial) agency, is a key component of Darwinian evolution and countless other natural and social phenomena. Yet a general ... More
Reliability study of series and parallel systems of heterogeneous component lifetimes under proportional odds modelDec 02 2016In this paper, we investigate various stochastic orderings for series and parallel systems with independent and heterogeneous components having lifetimes following the proportional odds model. We also investigate comparisons between system with heterogeneous ... More
Optimal discrimination designs for semi-parametric modelsDec 01 2016Much of the work in the literature on optimal discrimination designs assumes that the models of interest are fully specified, apart from unknown parameters in some models. Recent work allows errors in the models to be non-normally distributed but still ... More
Estimating a monotone probability mass function with known flat regionsDec 01 2016Dec 06 2016We propose a new estimator of a discrete monotone probability mass function with known flat regions. We analyse its asymptotic properties and compare its performance to the Grenander estimator and to the monotone rearrangement estimator.
Estimating a monotone probability mass function with known flat regionsDec 01 2016We propose a new estimator of a discrete monotone probability mass function with known flat regions. We analyse its asymptotic properties and compare its performance to the Grenander estimator and to the monotone rearrangement estimator.
Estimating a monotone probability mass function with known flat regionsDec 01 2016Dec 03 2016We propose a new estimator of a discrete monotone probability mass function with known flat regions. We analyse its asymptotic properties and compare its performance to the Grenander estimator and to the monotone rearrangement estimator.
Estimation and Model Identification of Locally Stationary Varying-Coefficient Additive ModelsDec 01 2016Nonparametric regression models with locally stationary covariates have received increasing interest in recent years. As a nice relief of "curse of dimensionality" induced by large dimension of covariates, additive regression model is commonly used. However, ... More
Inference for the mode of a log-concave densityNov 30 2016Dec 04 2016We study a likelihood ratio test for the location of the mode of a log-concave density. Our test is based on comparison of the log-likelihoods corresponding to the unconstrained maximum likelihood estimator of a log-concave density and the constrained ... More
Inference for the mode of a log-concave densityNov 30 2016We study a likelihood ratio test for the location of the mode of a log-concave density. Our test is based on comparison of the log-likelihoods corresponding to the unconstrained maximum likelihood estimator of a log-concave density and the constrained ... More
Mode-constrained estimation of a log-concave densityNov 30 2016Dec 04 2016We study nonparametric maximum likelihood estimation of a log-concave density function $f$ with a known mode $m$. We develop asymptotic theory for the mode-constrained estimator, including, consistency, global rates of convergence, and local rates of ... More
Mode-constrained estimation of a log-concave densityNov 30 2016We study nonparametric maximum likelihood estimation of a log-concave density function $f$ with a known mode $m$. We develop asymptotic theory for the mode-constrained estimator, including, consistency, global rates of convergence, and local rates of ... More
PCA from noisy, linearly reduced data: the diagonal caseNov 30 2016Suppose we observe data of the form $Y_i = D_i (S_i + \varepsilon_i) \in \mathbb{R}^p$ or $Y_i = D_i S_i + \varepsilon_i \in \mathbb{R}^p$, $i=1,\ldots,n$, where $D_i \in \mathbb{R}^{p\times p}$ are known diagonal matrices, $\varepsilon_i$ are noise, ... More
Quasi-invariance of countable products of Cauchy measures under translations and non-unitary dilationsNov 30 2016Consider an infinite sequence $\underline{U}=(U_n)_{n=1}^\infty$ of independent Cauchy random variables, defined by a sequence $\underline{\delta}$ of location parameters and a sequence $\underline{\gamma}$ of scale parameters. Let $\underline{V}$ be ... More
Regularized maximum likelihood estimation of covariance matrices of elliptical distributionsNov 30 2016The maximum likelihood principle is widely used in statistics, and the associated estimators often display good properties. indeed maximum likelihood estimators are guaranteed to be asymptotically efficient under mild conditions. However in some settings, ... More
Reducing bias in nonparametric density estimation via bandwidth dependent kernels: $L_1$ viewNov 30 2016We define a new bandwidth-dependent kernel density estimator that improves existing convergence rates for the bias, and preserves that of the variation, when the error is measured in $L_1$. No additional assumptions are imposed to the extant literature. ... More
The Dantzig selector for diffusion processes with covariatesNov 30 2016The Dantzig selector for a special parametric model of diffusion processes is studied in this paper. In our model, the diffusion coefficient is given as the exponential of the linear combination of other processes which are regarded as covariates. We ... More
Nonparametric Regression with Adaptive Truncation via a Convex Hierarchical PenaltyNov 30 2016Dec 01 2016We consider the problem of non-parametric regression with a potentially large number of covariates. We propose a convex, penalized estimation framework that is particularly well-suited for high-dimensional sparse additive models. The proposed approach ... More
Nonparametric Regression with Adaptive Truncation via a Convex Hierarchical PenaltyNov 30 2016We consider the problem of non-parametric regression with a potentially large number of covariates. We propose a convex, penalized estimation framework that is particularly well-suited for high-dimensional sparse additive models. The proposed approach ... More
Trimmed Conformal Prediction for High-Dimensional ModelsNov 29 2016In regression, conformal prediction is a general methodology to construct prediction intervals in a distribution-free manner. Although conformal prediction guarantees strong statistical property for predictive inference, its inherent computational challenge ... More
Best linear unbiased estimators in continuous time regression modelsNov 29 2016In this paper the problem of best linear unbiased estimation is investigated for continuous-time regression models. We prove several general statements concerning the explicit form of the best linear unbiased estimator (BLUE), in particular when the error ... More
Optimal adaptive estimation of linear functionals under sparsityNov 29 2016We consider the problem of estimation of a linear functional in the Gaussian sequence model where the unknown vector theta in R^d belongs to a class of s-sparse vectors with unknown s. We suggest an adaptive estimator achieving a non-asymptotic rate of ... More
Level sets and drift estimation for reflected Brownian motion with driftNov 29 2016We consider the estimation of the drift and the level sets of the stationary distri- bution of a Brownian motion with drift, reflected in the boundary of a compact set $S\subsetR^d$ , departing from the observation of a trajectory of this process. We ... More
A finite mixture model approach to regression under covariate misclassificationNov 28 2016This paper considers the problem of mismeasured categorical covariates in the context of regression modeling; if unaccounted for, such misclassification is known to result in misestimation of model parameters. Here, we exploit the fact that explicitly ... More
Simultaneous Clustering and Estimation of Heterogeneous Graphical ModelsNov 28 2016We consider joint estimation of multiple graphical models arising from heterogeneous and high-dimensional observations. Unlike most previous approaches which assume that the cluster structure is given in advance, an appealing feature of our method is ... More
Minimax Signal Detection Under Weak Noise AssumptionsNov 28 2016We consider minimax signal detection in the sequence model. Working with certain ellipsoids in the space of square-summable sequences of real numbers, with a ball of positive radius removed, we obtain upper and lower bounds for the minimax separation ... More
The dimple problem related to space-time modeling under the Lagrangian frameworkNov 28 2016Space-time covariance modeling under the Lagrangian framework has been especially popular for modeling phenomena with the presence of prevailing winds or ocean currents, which are incompatible with the assumption of full symmetry. In this work, we assess ... More