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On compatibility/incompatibility of two discrete probability distributions in the presence of incomplete specificationSep 18 2019Conditional specification of distributions is a developing area with many applications. In the finite discrete case, a variety of compatible conditions can be derived. In this paper, we propose an alternative approach to study the compatibility of two ... More
Inference on the change point with the jump size near the boundary of the region of detectability in high dimensional time series modelsSep 17 2019We develop a projected least squares estimator for the change point parameter in a high dimensional time series model with a potential change point. Importantly we work under the setup where the jump size may be near the boundary of the region of detectability. ... More
Minimax Confidence Intervals for the Sliced Wasserstein DistanceSep 17 2019The Wasserstein distance has risen in popularity in the statistics and machine learning communities as a useful metric for comparing probability distributions. We study the problem of uncertainty quantification for the Sliced Wasserstein distance--an ... More
Two-Sample Test Based on Classification ProbabilitySep 17 2019Robust classification algorithms have been developed in recent years with great success. We take advantage of this development and recast the classical two-sample test problem in the framework of classification. Based on the estimates of classification ... More
Efficient and Robust Estimation of Linear Regression with Normal ErrorsSep 17 2019Linear regression with normally distributed errors - including particular cases such as ANOVA, Student's t-test or location-scale inference - is a widely used statistical procedure. In this case the ordinary least squares estimator possesses remarkable ... More
The Mathematics of Benford's Law -- A PrimerSep 17 2019This article provides a concise overview of the main mathematical theory of Benford's law in a form accessible to scientists and students who have had first courses in calculus and probability. In particular, one of the main objectives here is to aid ... More
Estimation of Wasserstein distances in the Spiked Transport ModelSep 16 2019We propose a new statistical model, the spiked transport model, which formalizes the assumption that two probability distributions differ only on a low-dimensional subspace. We study the minimax rate of estimation for the Wasserstein distance under this ... More
Dirichlet Depths for Point ProcessSep 16 2019Statistical depths have been well studied for multivariate and functional data over the past few decades, but remain under-explored for point processes. A first attempt on the notion of point process depth was conducted recently where the depth was defined ... More
Improved estimation via model selection method for semimartingale regressions based on discrete dataSep 16 2019We consider the robust adaptive nonparametric estimation problem for a periodic function observed in the framework of a continuous time regression model with semimartingale noises.
Estimating change points in nonparametric time series regression modelsSep 16 2019In this paper we consider a regression model that allows for time series covariates as well as heteroscedasticity with a regression function that is modelled nonparametrically. We assume that the regression function changes at some unknown time $\lfloor ... More
On the Hurwitz zeta function with an application to the exponential-beta distributionSep 16 2019We prove a monotonicity property of the Hurwitz zeta function which, in turn, translates into a chain of inequalities for polygamma functions of different orders. We provide a probabilistic interpretation of our result by exploiting a connection between ... More
Inference for multiple object tracking: A Bayesian nonparametric approachSep 16 2019In recent years, multi object tracking (MOT) problem has drawn attention to it and has been studied in various research areas. However, some of the challenging problems including time dependent cardinality, unordered measurement set, and object labeling ... More
Higher Order Refinements by Bootstrap in Lasso and other Penalized Regression MethodsSep 14 2019Selection of important covariates and to drop the unimportant ones from a high-dimensional regression model is a long standing problem and hence have received lots of attention in the last two decades. After selecting the correct model, it is also important ... More
Relation between non-exchangeability and measures of concordance of copulasSep 14 2019An investigation is presented of how a comprehensive choice of five most important measures of concordance (namely Spearman's rho, Kendall's tau, Spearman's footrule, Gini's gamma, and Blomqvist's beta) relate to non-exchangeability, i.e., asymmetry on ... More
Sup-sums principles for F-divergence, Kullback--Leibler divergence, and new definition for t-entropySep 14 2019The article presents new sup-sums principles for integral F-divergence for arbitrary convex function F and arbitrary (not necessarily positive and absolutely continuous) measures. As applications of these results we derive the corresponding sup-sums principle ... More
Typical ranks in symmetric matrix completionSep 14 2019We study the problem of low-rank matrix completion for symmetric matrices. The minimum rank of a completion of a generic partially specified symmetric matrix depends only on the location of the specified entries, and not their values, if complex entries ... More
Confidence Tubes for Curves on SO(3) and Identification of Subject-Specific Gait Change after KneelingSep 14 2019In order to identify changes of gait patterns, e.g. due to prolonged occupational kneeling, which is believed to be major risk factor, among others, for the development of knee osteoarthritis, we develop confidence tubes for curves following a Gaussian ... More
Community Detection for Hypergraph Networks via Regularized Tensor Power IterationSep 14 2019To date, social network analysis has been largely focused on pairwise interactions. The study of higher-order interactions, via a hypergraph network, brings in new insights. We study community detection in a hypergraph network. A popular approach is to ... More
Some improvement on non-parametric estimation of income distribution and poverty indexSep 13 2019In this paper, we propose an estimator of Foster, Greer and Thorbecke class of measures $\displaystyle P(z,\alpha) = \int_0^{z}\Big(\frac{z-x}{z}\Big)^{\alpha}f(x)\, dx$, where $z>0$ is the poverty line, $f$ is the probabily density function of the income ... More
Some improvement on non-parametric estimation of income distribution and poverty indexSep 13 2019Sep 17 2019In this paper, we propose an estimator of Foster, Greer and Thorbecke class of measures $\displaystyle P(z,\alpha) = \int_0^{z}\Big(\frac{z-x}{z}\Big)^{\alpha}f(x)\, dx$, where $z>0$ is the poverty line, $f$ is the probabily density function of the income ... More
MACE: Multiscale Abrupt Change Estimation Under Complex Temporal DynamicsSep 13 2019We consider the problem of detecting abrupt changes in an otherwise smoothly evolving trend whilst the covariance and higher-order structures of the system can experience both smooth and abrupt changes over time. The number of abrupt change points is ... More
Testing Hypotheses about Covariance Matrices in General MANOVA DesignsSep 13 2019We introduce a unified approach to testing a variety of rather general null hypotheses that can be formulated in terms of covariances matrices. These include as special cases, for example, testing for equal variances, equal traces, or for elements of ... More
Uniform convergence rate of nonparametric maximum likelihood estimator for the current status data with competing risksSep 13 2019We study the uniform convergence rate of the nonparametric maximum likelihood estimator (MLE) for the sub-distribution functions in the current status data with competing risks model. It is known that the MLE have $L^2$-norm convergence rate $O_P(n^{-1/3})$ ... More
Estimating drift parameters in a non-ergodic Gaussian Vasicek-type modelSep 13 2019We study the problem of parameter estimation for a non-ergodic Gaussian Vasicek-type model defined as $dX_t=(\mu+\theta X_t)dt+dG_t,\ t\geq0$ with unknown parameters $\theta>0$ and $\mu\in\R$, where $G$ is a Gaussian process. We provide least square-type ... More
Bootstrapping the Operator Norm in High Dimensions: Error Estimation for Covariance Matrices and SketchingSep 13 2019Although the operator (spectral) norm is one of the most widely used metrics for covariance estimation, comparatively little is known about the fluctuations of error in this norm. To be specific, let $\hat\Sigma$ denote the sample covariance matrix of ... More
Two-sample tests for relevant differences in the eigenfunctions of covariance operatorsSep 13 2019This paper deals with two-sample tests for functional time series data, which have become widely available in conjunction with the advent of modern complex observation systems. Here, particular interest is in evaluating whether two sets of functional ... More
Generalized Records for Functional Time Series with Application to Unit Root TestsSep 13 2019A generalization of the definition of records to functional data is proposed. The definition is based on ranking curves using a notion of functional depth. This approach allows us to study the curves of the number of records over time. We focus on functional ... More
Compound Sequential Change Point Detection in Multiple Data StreamsSep 12 2019We consider sequential change point detection in multiple data streams, where each stream has its own change point. Once a change point is detected for a data stream, this stream is deactivated permanently. The goal is to maximize the normal operation ... More
Estimating Differential Latent Variable Graphical Models with Applications to Brain ConnectivitySep 12 2019Differential graphical models are designed to represent the difference between the conditional dependence structures of two groups, thus are of particular interest for scientific investigation. Motivated by modern applications, this manuscript considers ... More
A taxonomy of estimator consistency on discrete estimation problemsSep 12 2019We describe a four-level hierarchy mapping both all discrete estimation problems and all estimators on these problems, such that the hierarchy describes each estimator's consistency guarantees on each problem class. We show that no estimator is consistent ... More
Sharp Large Deviations for empirical correlation coefficientsSep 12 2019We study Sharp Large Deviations for Pearson's empirical correlation coefficients in the Spherical and Gaussian cases
Optimal choice of $k$ for $k$-nearest neighbor regressionSep 12 2019The $k$-nearest neighbor algorithm ($k$-NN) is a widely used non-parametric method for classification and regression. We study the mean squared error of the $k$-NN estimator when $k$ is chosen by leave-one-out cross-validation (LOOCV). Although it was ... More
A statistical methodology to select covariates in high-dimensional data under dependence. Application to the classification of genetic profiles in oncologySep 12 2019We propose a new methodology for selecting and ranking covariates associated with a variable of interest in a context of high-dimensional data under dependence but few observations. The methodology successively intertwines the clustering of covariates, ... More
A comparison of some conformal quantile regression methodsSep 12 2019We compare two recently proposed methods that combine ideas from conformal inference and quantile regression to produce locally adaptive and marginally valid prediction intervals under sample exchangeability (Romano et al., 2019; Kivaranovic et al., 2019). ... More
A refined determinantal inequality for correlation matricesSep 12 2019Olkin [3] obtained a neat upper bound for the determinant of a correlation matrix. In this note, we present an extension and improvement of his result.
The Global Markov Property for a Mixture of DAGsSep 12 2019Real causal processes may contain feedback loops and change over time. In this paper, we model cycles and non-stationary distributions using a mixture of directed acyclic graphs (DAGs). We then study the conditional independence (CI) relations induced ... More
The Global Markov Property for a Mixture of DAGsSep 12 2019Sep 13 2019Real causal processes may contain feedback loops and change over time. In this paper, we model cycles and non-stationary distributions using a mixture of directed acyclic graphs (DAGs). We then study the conditional independence (CI) relations induced ... More
Goodness-of-fit tests on manifoldsSep 11 2019We develop a general theory for the goodness-of-fit test to non-linear models. In particular, we assume that the observations are noisy samples of a sub-manifold defined by a non-linear map of some intrinsic structures. The observation noise is additive ... More
Aggregated Hold-OutSep 11 2019Aggregated hold-out (Agghoo) is a method which averages learning rules selected by hold-out (that is, cross-validation with a single split). We provide the first theoretical guarantees on Agghoo, ensuring that it can be used safely: Agghoo performs at ... More
Bayesian Inference on Volatility in the Presence of Infinite Jump Activity and Microstructure NoiseSep 11 2019Volatility estimation based on high-frequency data is key to accurately measure and control the risk of financial assets. A L\'{e}vy process with infinite jump activity and microstructure noise is considered one of the simplest, yet accurate enough, models ... More
Unified $\ell_{2\rightarrow\infty}$ Eigenspace Perturbation Theory for Symmetric Random MatricesSep 11 2019Modern applications in statistics, computer science and network science have seen tremendous values of finer matrix spectral perturbation theory. In this paper, we derive a generic $\ell_{2\rightarrow\infty}$ eigenspace perturbation bound for symmetric ... More
Distorted stochastic dominance: a generalized family of stochastic ordersSep 10 2019We study a generalized family of stochastic orders, semiparametrized by a distortion function H, namely H-distorted stochastic dominance, which may determine a continuum of dominance relations from the first- to the second-order stochastic dominance (and ... More
De-biased Machine Learning for CompliersSep 10 2019Instrumental variable identification is a concept in causal statistics for estimating the counterfactual effect of treatment D on output Y controlling for covariates X using observational data. Even when measurements of (Y,D) are confounded, the treatment ... More
Virtual Historical Simulation for estimating the conditional VaR of large portfoliosSep 10 2019In order to estimate the conditional risk of a portfolio's return, two strategies can be advocated. A multivariate strategy requires estimating a dynamic model for the vector of risk factors, which is often challenging, when at all possible, for large ... More
Targeted Random Projection for Prediction from High-Dimensional FeaturesSep 10 2019We consider the problem of computationally-efficient prediction with high dimensional and highly correlated predictors when accurate variable selection is effectively impossible. Direct application of penalization or Bayesian methods implemented with ... More
Optimality of the Subgradient Algorithm in the Stochastic SettingSep 10 2019Recently Jaouad Mourtada and St\' ephane Ga\"iffas showed the anytime hedge algorithm has pseudo-regret $O(\log (d) / \Delta)$ if the cost vectors are generated by an i.i.d sequence in the cube $[0,1]^d$. Here $d$ is the dimension and $\Delta$ the suboptimality ... More
On Robust Spectrum Sensing Using M-estimators of Covariance MatrixSep 10 2019In this paper, we consider the spectrum sensing in cognitive radio networks when the impulsive noise appears. We propose a class of blind and robust detectors using M-estimators in eigenvalue based spectrum sensing method. The conventional eigenvalue ... More
Robust Multivariate Estimation Based On Statistical Data Depth FiltersSep 10 2019In the classical contamination models, such as the gross-error (Huber and Tukey contamination model or Case-wise Contamination), observations are considered as the units to be identified as outliers or not, this model is very useful when the number of ... More
Convergence of least squares estimators in the adaptive Wynn algorithm for a class of nonlinear regression modelsSep 09 2019The paper continues the authors' work on the adaptive Wynn algorithm in a nonlinear regression model. In the present paper it is shown that if the mean response function satisfies a condition of `saturated identifiability', which was introduced by Pronzato ... More
Isotonic Distributional RegressionSep 09 2019Isotonic distributional regression (IDR) is a powerful nonparametric technique for the estimation of conditional distributions under order restrictions. In a nutshell, IDR learns conditional distributions that are calibrated, and simultaneously optimal ... More
Inference In General Single-Index Models Under High-dimensional Symmetric DesignsSep 08 2019We consider the problem of statistical inference for a finite number of covariates in a generalized single-index model with p > n covariates and unknown (potentially random) link function under an elliptically symmetric design. Under elliptical symmetry, ... More
A hypothesis-testing perspective on the G-normal distribution theorySep 08 2019The G-normal distribution was introduced by Peng [2007] as the limiting distribution in the central limit theorem for sublinear expectation spaces. Equivalently, it can be interpreted as the solution to a stochastic control problem where we have a sequence ... More
Probabilistic Convergence and Stability of Random Mapper GraphsSep 08 2019We study the probabilistic convergence between the mapper graph and the Reeb graph of a topological space $\mathbb{X}$ equipped with a continuous function $f: \mathbb{X} \rightarrow \mathbb{R}$. We first give a categorification of the mapper graph and ... More
Concentration of kernel matrices with application to kernel spectral clusteringSep 07 2019We study the concentration of random kernel matrices around their mean. We derive nonasymptotic exponential concentration inequalities for Lipschitz kernels assuming that the data points are independent draws from a class of multivariate distributions ... More
On the Optimality of Gaussian Kernel Based Nonparametric Tests against Smooth AlternativesSep 07 2019Nonparametric tests via kernel embedding of distributions have witnessed a great deal of practical successes in recent years. However, statistical properties of these tests are largely unknown beyond consistency against a fixed alternative. To fill in ... More
Community detection in inhomogeneous random graphsSep 07 2019We study the problem of detecting whether an inhomogeneous random graph contains a planted community. Specifically, we observe a single realization of a graph. Under the null hypothesis, this graph is a sample from an inhomogeneous random graph, whereas ... More
Bayesian Design of Sampling Set for Bandlimited Graph SignalsSep 07 2019The design of sampling set (DoS) for bandlimited graph signals (GS) has been extensively studied in recent years, but few of them exploit the benefits of the stochastic prior of GS. In this work, we introduce the optimization framework for Bayesian DoS ... More
On the Estimation of Network Complexity: Dimension of GraphonsSep 06 2019Network complexity has been studied for over half a century and has found a wide range of applications. Many methods have been developed to characterize and estimate the complexity of networks. However, there has been little research with statistical ... More
Optimal unbiased estimators via convex hullsSep 06 2019Necessary and sufficient conditions for the square-integrability of recently proposed unbiased estimators are established. A geometric characterization of a distribution that optimizes the performance of these estimators is given. An algorithm based on ... More
Generalization of the simplicial depth: no vanishment outside the convex hull of the distribution supportSep 06 2019The simplicial depth, like other relevant multivariate statistical data depth functions, vanishes right outside the convex hull of the support of the distribution with respect to which the depth is computed. This is problematic when it is required to ... More
Asymptotic Optimality in Byzantine Distributed Quickest Change DetectionSep 06 2019The Byzantine distributed quickest change detection (BDQCD) is studied, where a fusion center monitors the occurrence of an abrupt event through a bunch of distributed sensors that may be compromised. We first consider the binary hypothesis case where ... More
Block bootstrap optimality for density estimation with dependent dataSep 05 2019Accurate approximation of the sampling distribution of nonparametric kernel density estimators is crucial for many statistical inference problems. Since these estimators have complex asymptotic distributions, bootstrap methods are often used for this ... More
Number of Sign Changes: Segment of AR(1)Sep 05 2019Let $X_{t}$ denote a stationary first-order autoregressive process. Consider $n$ contiguous observations (in time $t$) of the series (e.g., $X_{1}, ..., X_{n}$). Let its mean be zero and its lag-one serial correlation be $\rho$, which satisfies $|\rho| ... More
Smooth Contextual Bandits: Bridging the Parametric and Non-differentiable Regret RegimesSep 05 2019We study a nonparametric contextual bandit problem where the expected reward functions belong to a H\"older class with smoothness parameter $\beta$. We show how this interpolates between two extremes that were previously studied in isolation: non-differentiable ... More
The distribution of Yule's 'nonsense correlation'Sep 05 2019In 2017, the authors of~\citet{ernst2017yule} explicitly computed the second moment of Yule's "nonsense correlation," offering the first mathematical explanation of Yule's 1926 empirical finding of nonsense correlation.~\citep{yule1926}. The present work ... More
Vector-valued Generalised Ornstein-Uhlenbeck ProcessesSep 05 2019Generalisations of the Ornstein-Uhlenbeck process defined through Langevin equation $dU_t = - \Theta U_t dt + dG_t,$ such as fractional Ornstein-Uhlenbeck processes, have recently received a lot of attention in the literature. In particular, estimation ... More
Further study on inferential aspects of log-Lindley distribution with an application of stress-strength reliability in insuranceSep 05 2019The log-Lindley distribution was recently introduced in the literature as a viable alternative to the Beta distribution. This distribution has a simple structure and possesses useful theoretical properties relevant in insurance. Classical estimation methods ... More
A new reproducing kernel based nonlinear dimension reduction method for survival dataSep 05 2019Based on the theories of sliced inverse regression (SIR) and reproducing kernel Hilbert space (RKHS), a new approach RDSIR (RKHS-based Double SIR) to nonlinear dimension reduction for survival data is proposed and discussed. An isometrically isomorphism ... More
Optimal UCB Adjustments for Large Arm SizesSep 05 2019The regret lower bound of Lai and Robbins (1985), the gold standard for checking optimality of bandit algorithms, considers arm size fixed as sample size goes to infinity. We show that when arm size increases polynomially with sample size, a surprisingly ... More
Theory of high-dimensional outliersSep 04 2019This study concerns the issue of high dimensional outliers which are challenging to distinguish from inliers due to the special structure of high dimensional space. We introduce a new notion of high dimensional outliers that embraces various types and ... More
On Least Squares Estimation under Heteroscedastic and Heavy-Tailed ErrorsSep 04 2019We consider least squares estimation in a general nonparametric regression model. The rate of convergence of the least squares estimator (LSE) for the unknown regression function is well studied when the errors are sub-Gaussian. We find upper bounds on ... More
On Least Squares Estimation under Heteroscedastic and Heavy-Tailed ErrorsSep 04 2019Sep 14 2019We consider least squares estimation in a general nonparametric regression model. The rate of convergence of the least squares estimator (LSE) for the unknown regression function is well studied when the errors are sub-Gaussian. We find upper bounds on ... More
Semiparametric Inference for Non-monotone Missing-Not-at-Random Data: the No Self-Censoring ModelSep 04 2019We study the identification and estimation of statistical functionals of multivariate data missing non-monotonically and not-at-random, taking a semiparametric approach. Specifically, we assume that the missingness mechanism satisfies what has been previously ... More
Learning Distributions Generated by One-Layer ReLU NetworksSep 04 2019We consider the problem of estimating the parameters of a $d$-dimensional rectified Gaussian distribution from i.i.d. samples. A rectified Gaussian distribution is defined by passing a standard Gaussian distribution through a one-layer ReLU neural network. ... More
Subset Multivariate Collective And Point Anomaly DetectionSep 04 2019In recent years, there has been a growing interest in identifying anomalous structure within multivariate data streams. We consider the problem of detecting collective anomalies, corresponding to intervals where one or more of the data streams behaves ... More
Testing nonparametric shape restrictionsSep 04 2019We describe and examine a test for shape constraints, such as monotonicity, convexity (or both simultaneously), U-shape, S-shape and others, in a nonparametric framework using partial sums empirical processes. We show that, after a suitable transformation, ... More
Rates of Convergence for Large-scale Nearest Neighbor ClassificationSep 03 2019Nearest neighbor is a popular class of classification methods with many desirable properties. For a large data set which cannot be loaded into the memory of a single machine due to computation, communication, privacy, or ownership limitations, we consider ... More
On perfectness in Gaussian graphical modelsSep 03 2019Knowing when a graphical model is perfect to a distribution is essential in order to relate separation in the graph to conditional independence in the distribution, and this is particularly important when performing inference from data. When the model ... More
Moment convergence of the generalized maximum composite likelihood estimators for determinantal point processesSep 03 2019The maximum composite likelihood estimator for parametric models of determinantal point processes (DPPs) is discussed. Since the joint intensities of these point processes are given by determinant of positive definite kernels, we have the explicit form ... More
Starting CLuP with polytope relaxationSep 03 2019The Controlled Loosening-up (CLuP) mechanism that we recently introduced in \cite{Stojnicclupint19} is a generic concept that can be utilized to solve a large class of problems in polynomial time. Since it relies in its core on an iterative procedure, ... More
Complexity analysis of the Controlled Loosening-up (CLuP) algorithmSep 03 2019Sep 04 2019In our companion paper \cite{Stojnicclupint19} we introduced a powerful mechanism that we referred to as the Controlled Loosening-up (CLuP) for handling MIMO ML-detection problems. It turned out that the algorithm has many remarkable features and one ... More
Controlled Loosening-up (CLuP) -- achieving exact MIMO ML in polynomial timeSep 03 2019In this paper we attack one of the most fundamental signal processing/informaton theory problems, widely known as the MIMO ML-detection. We introduce a powerful Random Duality Theory (RDT) mechanism that we refer to as the Controlled Loosening-up (CLuP) ... More
A Diffusion Process Perspective on Posterior Contraction Rates for ParametersSep 03 2019We show that diffusion processes can be exploited to study the posterior contraction rates of parameters in Bayesian models. By treating the posterior distribution as a stationary distribution of a stochastic differential equation (SDE), posterior convergence ... More
Random Graph Models and MatchingsSep 02 2019In this paper we will provide an introductory understanding of random graph models, and matchings in the case of Erdos-Renyi random graphs. We will provide a synthesis of background theory to this end. We will further examine pertinent recent results ... More
Consistency of Ranking EstimatorsSep 02 2019The ranking problem is to order a collection of units by some unobserved parameter, based on observations from the associated distribution. This problem arises naturally in a number of contexts, such as business, where we may want to rank potential projects ... More
Statistics of Gaussians on local fields and their tropicalizationsSep 02 2019We study multivariate Gaussian distributions on local fields such as the field of p-adic numbers. We introduce the Bruhat-Tits building as a parameter space for Gaussian distributions and study some classic statistical problems in this setting. Finally ... More
Central limit theorems for discretized occupation time functionalsSep 01 2019The approximation of integral type functionals is studied for discrete observations of a continuous It\^o semimartingale. Based on novel approximations in the Fourier domain, central limit theorems are proved for $L^2$-Sobolev functions with fractional ... More
Stability of the Cut Locus and a Central Limit Theorem for Fréchet Means of Riemannian ManifoldsSep 01 2019Sep 04 2019We obtain a Central Limit Theorem for closed Riemannian manifolds, clarifying along the way the geometric meaning of some of the hypotheses in Bhattacharya and Lin's Omnibus Central Limit Theorem for Fr\'echet means. We obtain our CLT assuming certain ... More
Anti-MANOVA on Compact Manifolds with Applications to 3D Projective Shape AnalysisSep 01 2019Methods of hypotheses testing for equality of extrinsic antimeans on compact manifolds are unveiled in this paper. The two and multiple sample problem for antimeans on compact manifolds is addressed for large samples via asymptotic distributions, as well ... More
A Note on New Bernstein-type Inequalities for the Log-likelihood Function of Bernoulli VariablesAug 31 2019We prove a new Bernstein-type inequality for the log-likelihood function of Bernoulli variables. In contrast to classical Bernstein's inequality and Hoeffding's inequality when applied to the log-likelihood, the new bound is independent of the parameters ... More
Convergence of Gaussian Process Regression with Estimated Hyper-parameters and Applications in Bayesian Inverse ProblemsAug 31 2019This work is concerned with the convergence of Gaussian process regression. A particular focus is on hierarchical Gaussian process regression, where hyper-parameters appearing in the mean and covariance structure of the Gaussian process emulator are a-priori ... More
Convergence of Gaussian Process Regression with Estimated Hyper-parameters and Applications in Bayesian Inverse ProblemsAug 31 2019Sep 10 2019This work is concerned with the convergence of Gaussian process regression. A particular focus is on hierarchical Gaussian process regression, where hyper-parameters appearing in the mean and covariance structure of the Gaussian process emulator are a-priori ... More
Minimum $L^q$-distance estimators for non-normalized parametric modelsAug 30 2019We propose and investigate a new estimation method for the parameters of models consisting of smooth density functions on the positive half axis. The procedure is based on a recently introduced characterization result for the respective probability distributions, ... More
The extended xgamma distributionAug 30 2019This article aims to introduced a new distribution named as extended xgamma (EXg) distribution. This generalization is derived from xgamma distribution (Xg), a special finite mixture of exponential and gamma distributions [see, Sen et al. ($2016$)]. Some ... More
Composite likelihood methods for histogram-valued random variablesAug 30 2019Symbolic data analysis has been proposed as a technique for summarising large and complex datasets into a much smaller and tractable number of distributions -- such as random rectangles or histograms -- each describing a portion of the larger dataset. ... More
Fraudulent White Noise: Flat power spectra belie arbitrarily complex processesAug 29 2019Power spectral densities are a common, convenient, and powerful way to analyze signals. So much so that they are now broadly deployed across the sciences and engineering---from quantum physics to cosmology, and from crystallography to neuroscience to ... More
Nearly-Linear uncertainty measuresAug 29 2019Several easy to understand and computationally tractable imprecise probability models, like the Pari-Mutuel model, are derived from a given probability measure P_0. In this paper we investigate a family of such models, called Nearly-Linear (NL). They ... More
Deep Learning and MARS: A ConnectionAug 29 2019Sep 08 2019We consider least squares regression estimates using deep neural networks. We show that these estimates satisfy an oracle inequality, which implies that (up to a logarithmic factor) the error of these estimates is at least as small as the optimal possible ... More
Deep Learning and MARS: A ConnectionAug 29 2019We consider least squares regression estimates using deep neural networks. We show that these estimates satisfy an oracle inequality, which implies that (up to a logarithmic factor) the error of these estimates is at least as small as the optimal possible ... More
On the rate of convergence of fully connected very deep neural network regression estimatesAug 29 2019Recent results in nonparametric regression show that deep learning, i.e., neural networks estimates with many hidden layers, are able to circumvent the so-called curse of dimensionality in case that suitable restrictions on the structure of the regression ... More