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Probability inequalities for high dimensional time series under a triangular array frameworkJul 15 2019Study of time series data often involves measuring the strength of temporal dependence, on which statistical properties like consistency and central limit theorem are built. Historically, various dependence measures have been proposed. In this note, we ... More
Shadow Simulated Annealing algorithm: a new tool for global optimisation and statistical inferenceJul 15 2019This paper develops a new global optimisation method that applies to a family of criteria that are not entirely known. This family includes the criteria obtained from the class of posteriors that have nor-malising constants that are analytically not tractable. ... More
A Simple Uniformly Valid Test for InequalitiesJul 15 2019We propose a new test for inequalities that is simple and uniformly valid. The test compares the likelihood ratio statistic to a chi-squared critical value, where the degrees of freedom is the rank of the active inequalities. This test requires no tuning ... More
Pointwise adaptive kernel density estimation under local approximate differential privacyJul 14 2019We consider non-parametric density estimation in the framework of local approximate differential privacy. In contrast to centralized privacy scenarios with a trusted curator, in the local setup anonymization must be guaranteed already on the individual ... More
A new approach to Poissonian two-armed bandit problemJul 13 2019We consider a continuous time two-armed bandit problem in which incomes are described by Poissonian processes. We develop Bayesian approach with arbitrary prior distribution. We present two versions of recursive equation for determination of Bayesian ... More
Fisher-Rao Geometry and Jeffreys Prior for Pareto DistributionJul 13 2019In this paper, we investigate the Fisher-Rao geometry of the two-parameter family of Pareto distribution. We prove that its geometrical structure is isometric to the Poincar\'e upper half-plane model, and then study the corresponding geometrical features ... More
Estimating densities with nonlinear support using Fisher-Gaussian kernelsJul 12 2019Current tools for multivariate density estimation struggle when the density is concentrated near a nonlinear subspace or manifold. Most approaches require choice of a kernel, with the multivariate Gaussian by far the most commonly used. Although heavy-tailed ... More
Asymptotics for Spherical Functional AutoregressionsJul 12 2019In this paper, we investigate a class of spherical functional autoregressive processes, and we discuss the estimation of the corresponding autoregressive kernels. In particular, we first establish a consistency result (in sup and mean-square norm), then ... More
Path Weights in Concentration GraphsJul 12 2019A graphical model provides a compact and efficient representation of the association structure of a multivariate distribution by means of a graph. Relevant features of the distribution are represented by vertices, edges and other higher-order graphical ... More
Gittins' theorem under uncertaintyJul 12 2019We study dynamic allocation problems for discrete time multi-armed bandits under uncertainty, based on the the theory of nonlinear expectations. We show that, under strong independence of the bandits and with some relaxation in the definition of optimality, ... More
Statistical inference for piecewise normal distributions and stochastic variational inequalitiesJul 11 2019In this paper we first provide a method to compute confidence intervals for the center of a piecewise normal distribution given a sample from this distribution, under certain assumptions. We then extend this method to an asymptotic setting, and apply ... More
Low-rank matrix completion and denoising under Poisson noiseJul 11 2019This paper considers the problem of estimating a low-rank matrix from the observation of all, or a subset, of its entries in the presence of Poisson noise. When we observe all the entries, this is a problem of matrix denoising; when we observe only a ... More
Gain with no Pain: Efficient Kernel-PCA by Nyström SamplingJul 11 2019In this paper, we propose and study a Nystr\"om based approach to efficient large scale kernel principal component analysis (PCA). The latter is a natural nonlinear extension of classical PCA based on considering a nonlinear feature map or the corresponding ... More
Estimating the division rate from indirect measurements of single cellsJul 11 2019Is it possible to estimate the dependence of a growing and dividing population on a given trait in the case where this trait is not directly accessible by experimental measurements, but making use of measurements of another variable? This article adresses ... More
Directing Power Towards Sub-AlternativesJul 11 2019This paper proposes a novel test statistic for testing a potentially high-dimensional parameter vector. To derive the statistic, I generalize the Mahalanobis distance to measure length in a direction of interest. The test statistic is the sample analogue ... More
Nonparametric estimation of the conditional density function with right-censored and dependent dataJul 10 2019In this paper, we study the local constant and the local linear estimators of the conditional density function with right-censored data which exhibit some type of dependence. It is assumed that the observations form a stationary $\alpha-$mixing sequence. ... More
Tails of Triangular FlowsJul 10 2019Triangular maps are a construct in probability theory that allows the transformation of any source density to any target density. We consider flow based models that learn these triangular transformations which we call triangular flows and study the properties ... More
Optimal Chernoff and Hoeffding Bounds for Finite Markov ChainsJul 10 2019This paper develops an optimal Chernoff type bound for the probabilities of large deviations of sums $\sum_{k=1}^n f (X_k)$ where $f$ is a real-valued function and $(X_k)_{k \in \mathbb{N}_0}$ is a finite Markov chain with an arbitrary initial distribution ... More
Convergence Rates for Gaussian Mixtures of ExpertsJul 09 2019We provide a theoretical treatment of over-specified Gaussian mixtures of experts with covariate-free gating networks. We establish the convergence rates of the maximum likelihood estimation (MLE) for these models. Our proof technique is based on a novel ... More
A Bayesian Approach for Analyzing Data on the Stiefel ManifoldJul 09 2019Directional data emerges in a wide array of applications, ranging from atmospheric sciences to medical imaging. Modeling such data, however, poses unique challenges by virtue of their being constrained to non-Euclidean spaces like manifolds. Here, we ... More
Dreaming machine learning: Lipschitz extensions for reinforcement learning on financial marketsJul 09 2019We develop a new topological structure for the construction of a reinforcement learning model in the framework of financial markets. It is based on Lipschitz type extension of reward functions defined in metric spaces. Using some known states of a dynamical ... More
Optimal experimental designs for treatment contrasts in heteroscedastic models with covariatesJul 09 2019In clinical trials, the response of a given subject often depends on the selected treatment as well as on some covariates. We study optimal approximate designs of experiments in the models with treatment and covariate effects. We allow for the variances ... More
Nonconvex Regularized Robust Regression with Oracle Properties in Polynomial TimeJul 09 2019This paper investigates tradeoffs among optimization errors, statistical rates of convergence and the effect of heavy-tailed random errors for high-dimensional adaptive Huber regression with nonconvex regularization. When the additive errors in linear ... More
Bayesian approach for inverse obstacle scattering with Poisson dataJul 09 2019We consider an acoustic obstacle reconstruction problem with Poisson data. Due to the stochastic nature of the data, we tackle this problem in the framework of Bayesian inversion. The unknown obstacle is parameterized in its angular form. The prior for ... More
Residual EntropyJul 08 2019We describe an approach to improving model fitting and model generalization that considers the entropy of distributions of modelling residuals. We use simple simulations to demonstrate the observational signatures of overfitting on ordered sequences of ... More
Multi-Scale Vector Quantization with Reconstruction TreesJul 08 2019We propose and study a multi-scale approach to vector quantization. We develop an algorithm, dubbed reconstruction trees, inspired by decision trees. Here the objective is parsimonious reconstruction of unsupervised data, rather than classification. Contrasted ... More
Statistical Analysis of Nearest Neighbor Methods for Anomaly DetectionJul 08 2019Nearest-neighbor (NN) procedures are well studied and widely used in both supervised and unsupervised learning problems. In this paper we are concerned with investigating the performance of NN-based methods for anomaly detection. We first show through ... More
Asymptotic Bayes risk for Gaussian mixture in a semi-supervised settingJul 08 2019Semi-supervised learning (SSL) uses unlabeled data for training and has been shown to greatly improve performances when compared to a supervised approach on the labeled data available. This claim depends both on the amount of labeled data available and ... More
Comparing EM with GD in Mixture Models of Two ComponentsJul 08 2019The expectation-maximization (EM) algorithm has been widely used in minimizing the negative log likelihood (also known as cross entropy) of mixture models. However, little is understood about the goodness of the fixed points it converges to. In this paper, ... More
Testing Mixtures of Discrete DistributionsJul 06 2019There has been significant study on the sample complexity of testing properties of distributions over large domains. For many properties, it is known that the sample complexity can be substantially smaller than the domain size. For example, over a domain ... More
Towards Testing Monotonicity of Distributions Over General PosetsJul 06 2019In this work, we consider the sample complexity required for testing the monotonicity of distributions over partial orders. A distribution $p$ over a poset is monotone if, for any pair of domain elements $x$ and $y$ such that $x \preceq y$, $p(x) \leq ... More
Convergence Analysis of a Collapsed Gibbs Sampler for Bayesian Vector AutoregressionsJul 06 2019We propose a collapsed Gibbs sampler for Bayesian vector autoregressions with predictors, or exogenous variables, and study the proposed algorithm's convergence properties. The Markov chain generated by our algorithm converges to its stationary distribution ... More
Estimating location parameters in entangled single-sample distributionsJul 06 2019We consider the problem of estimating the common mean of independently sampled data, where samples are drawn in a possibly non-identical manner from symmetric, unimodal distributions with a common mean. This generalizes the setting of Gaussian mixture ... More
Posterior Convergence of $α$-Stable SheetsJul 06 2019This paper is concerned with the theoretical understanding of $\alpha$-stable sheets $U$ on $\mathbb{R}^d$. Our motivation for this is in the context of Bayesian inverse problems, where we consider these processes as prior distributions, aiming to quantify ... More
Posterior Convergence Analysis of $α$-Stable SheetsJul 06 2019Jul 11 2019This paper is concerned with the theoretical understanding of $\alpha$-stable sheets $U$ on $\mathbb{R}^d$. Our motivation for this is in the context of Bayesian inverse problems, where we consider these processes as prior distributions, aiming to quantify ... More
Posterior Convergence Analysis of $α$-Stable SheetsJul 06 2019Jul 09 2019This paper is concerned with the theoretical understanding of $\alpha$-stable sheets $U$ on $\mathbb{R}^d$. Our motivation for this is in the context of Bayesian inverse problems, where we consider these processes as prior distributions, aiming to quantify ... More
Improving Lasso for model selection and predictionJul 05 2019It is known that the Thresholded Lasso (TL), SCAD or MCP correct intrinsic estimation bias of the Lasso. In this paper we propose an alternative method of improving the Lasso for predictive models with general convex loss functions which encompass normal ... More
On Finite Exchangeability and Conditional IndependenceJul 05 2019We study the independence structure of finitely exchangeable distributions over random vectors and random networks. In particular, we provide necessary and sufficient conditions for an exchangeable vector so that its elements are completely independent ... More
On the Glivenko-Cantelli theorem for the functional empirical process using associated sequencesJul 05 2019Using a general strong law of large number proved by Sangare and Lo in \cite% {sanglo} and the entropy numbers, we provide a functional Glivenko-Cantelli theorem for arbitrary random variables (rv's).
A quantitative Mc Diarmid's inequality for geometrically ergodic Markov chainsJul 05 2019We state and prove a quantitative version of the bounded difference inequality for geometrically ergodic Markov chains. Our proof uses the same martingale decomposition as \cite{MR3407208} but, compared to this paper, the exact coupling argument is modified ... More
The adaptive Wynn-algorithm in generalized linear models with univariate responseJul 05 2019For a nonlinear regression model the information matrices of designs depend on the parameter of the model. The adaptive Wynn-algorithm for D-optimal design estimates the parameter at each step on the basis of the employed design points and observed responses ... More
Algorithms of Robust Stochastic Optimization Based on Mirror Descent MethodJul 05 2019We propose an approach to construction of robust non-Euclidean iterative algorithms for convex composite stochastic optimization based on truncation of stochastic gradients. For such algorithms, we establish sub-Gaussian confidence bounds under weak assumptions ... More
Importance of Small Probability Events in Big Data: Information Measures, Applications, and ChallengesJul 05 2019In many applications (e.g., anomaly detection and security systems) of smart cities, rare events dominate the importance of the total information of big data collected by Internet of Things (IoTs). That is, it is pretty crucial to explore the valuable ... More
Importance of Small Probability Events in Big Data: Information Measures, Applications, and ChallengesJul 05 2019Jul 08 2019In many applications (e.g., anomaly detection and security systems) of smart cities, rare events dominate the importance of the total information of big data collected by Internet of Things (IoTs). That is, it is pretty crucial to explore the valuable ... More
The Geometry of Community Detection via the MMSE MatrixJul 04 2019The information-theoretic limits of community detection have been studied extensively for network models with high levels of symmetry or homogeneity. The contribution of this paper is to study a broader class of network models that allow for variability ... More
Bayes factors with (overly) informative priorsJul 04 2019Priors in which a large number of parameters are specified to be independent are dangerous; they make it hard to learn from data. I present a couple of examples from the literature and work through a bit of large sample theory to show what happens.
Bayes factors with (overly) informative priorsJul 04 2019Jul 06 2019Priors in which a large number of parameters are specified to be independent are dangerous; they make it hard to learn from data. I present a couple of examples from the literature and work through a bit of large sample theory to show what happens.
Graphical Criteria for Efficient Total Effect Estimation via Adjustment in Causal Linear ModelsJul 04 2019Covariate adjustment is commonly used for total causal effect estimation. In recent years, graphical criteria have been developed to identify all covariate sets that can be used for this purpose. Different valid adjustment sets typically provide causal ... More
Construction of Blocked Factorial Designs to Estimate Main Effects and Selected Two-Factor InteractionsJul 04 2019Two-level factorial designs are widely used in industrial experiments. For processes involving \(n\) factors, the construction of designs comprising \(2^n\) and \(2^{n-p}\) factorials, arranged in blocks of size \(2^q\) is investigated. The aim is to ... More
Markov Decision Processes under AmbiguityJul 04 2019We consider statistical Markov Decision Processes where the decision maker is risk averse against model ambiguity. The latter is given by an unknown parameter which influences the transition law and the cost functions. Risk aversion is either measured ... More
Randomized sequential importance sampling for estimating the number of perfect matchings in bipartite graphsJul 04 2019We introduce novel randomized sequential importance sampling algorithms for estimating the number of perfect matchings in bipartite graphs. In analyzing their performance, we prove various non-standard central limit theorems, via limit theory for random ... More
Consistent Regression using Data-Dependent CoveringsJul 04 2019In this paper, we introduce a novel method to generate interpretable regression function estimators. The idea is based on called data-dependent coverings. The aim is to extract from the data a covering of the feature space instead of a partition. The ... More
Estimation of common change point and isolation of changed panels after sequential detectionJul 03 2019Quick detection of common changes is critical in sequential monitoring of multi-stream data where a common change is referred as a change that only occurs in a portion of panels. After a common change is detected by using a combined CUSUM-SR procedure, ... More
Understanding Phase Transitions via Mutual Information and MMSEJul 03 2019The ability to understand and solve high-dimensional inference problems is essential for modern data science. This article examines high-dimensional inference problems through the lens of information theory and focuses on the standard linear model as ... More
Large Deviations of the Estimated Cumulative Hazard RateJul 03 2019Survivorship analysis allows to statistically analyze situations that can be modeled as waiting times to an event. These waiting times are characterized by the cumulative hazard rate, which can be estimated by the Nelson-Aalen estimator or diverse confidence ... More
Bounding quantiles of Wasserstein distance between true and empirical measureJul 03 2019Consider the empirical measure, $\hat{\mathbb{P}}_N$, associated to $N$ i.i.d. samples of a given probability distribution $\mathbb{P}$ on the unit interval. For fixed $\mathbb{P}$ the Wasserstein distance between $\hat{\mathbb{P}}_N$ and $\mathbb{P}$ ... More
Mid-quantile regression for discrete responsesJul 03 2019We develop quantile regression methods for discrete responses by extending Parzen's definition of marginal mid-quantiles. As opposed to existing approaches, which are based on either jittering or latent constructs, we use interpolation and define the ... More
Unbiased Estimation of the Reciprocal Mean for Non-negative Random VariablesJul 03 2019Many simulation problems require the estimation of a ratio of two expectations. In recent years Monte Carlo estimators have been proposed that can estimate such ratios without bias. We investigate the theoretical properties of such estimators for the ... More
Estimating a probability of failure with the convex order in computer experimentsJul 03 2019This paper deals with the estimation of a failure probability of an industrial product. To be more specific, it is defined as the probability that the output of a physical model, with random input variables, exceeds a threshold. The model corresponds ... More
Deviation inequalities for separately Lipschitz functionals of composition of random functionsJul 03 2019We consider a class of non-homogeneous Markov chains, that contains many natural examples. Next, using martingale methods, we establish some deviation and moment inequalities for separately Lipschitz functions of such a chain, under moment conditions ... More
Sparse High-Dimensional Isotonic RegressionJul 03 2019We consider the problem of estimating an unknown coordinate-wise monotone function given noisy measurements, known as the isotonic regression problem. Often, only a small subset of the features affects the output. This motivates the sparse isotonic regression ... More
Causal models on probability spacesJul 02 2019We describe the interface between measure theoretic probability and causal inference by constructing causal models on probability spaces within the potential outcomes framework. We find that measure theory provides a precise and instructive language for ... More
Double Cross Validation for the Number of Factors in Approximate Factor ModelsJul 02 2019Determining the number of factors is essential to factor analysis. In this paper, we propose {an efficient cross validation (CV)} method to determine the number of factors in approximate factor models. The method applies CV twice, first along the directions ... More
Elicitability and Identifiability of Systemic Risk Measures and other Set-Valued FunctionalsJul 02 2019This paper is concerned with a two-fold objective. Firstly, we establish elicitability and identifiability results for systemic risk measures introduced in Feinstein, Rudloff and Weber (2017). Specifying the entire set of capital allocations adequate ... More
Specification testing in semi-parametric transformation modelsJul 02 2019In transformation regression models the response is transformed before fitting a regression model to covariates and transformed response. We assume such a model where the errors are independent from the covariates and the regression function is modeled ... More
The generalized orthogonal Procrustes problem in the high noise regimeJul 02 2019We consider the problem of estimating a cloud of points from numerous noisy observations of that cloud after unknown rotations, and possibly reflections. This is an instance of the general problem of estimation under group action, originally inspired ... More
Robust analogues to the Coefficient of VariationJul 02 2019The coefficient of variation (CV) is commonly used to measure relative dispersion. However, since it is based on the sample mean and standard deviation, outliers can adversely affect the CV. Additionally, for skewed distributions the mean and standard ... More
Multiple Bayesian Filtering as Message PassingJul 01 2019In this manuscript, a general method for deriving filtering algorithms that involve a network of interconnected Bayesian filters is proposed. This method is based on the idea that the processing accomplished inside each of the Bayesian filters and the ... More
A greedy algorithm for sparse precision matrix approximationJul 01 2019Precision matrix estimation is an important problem in statistical data analysis. This paper introduces a fast sparse precision matrix estimation algorithm, namely GISS$^{{\rho}}$, which is originally introduced for compressive sensing. The algorithm ... More
Sparse regular variationJul 01 2019Regular variation provides a convenient theoretical framework to study large events. In the multivariate setting, the dependence structure of the positive extremes is characterized by a measure-the spectral measure-defined on the positive orthant of the ... More
Power Lindley distribution and software metricsJul 01 2019The Lindley distribution and its numerous generalizations are widely used in statistical and engineering practice. Recently, a power transformation of Lindley distribution, called the power Lindley distribution, has been introduced by M. E. Ghitany et ... More
Bounding Causes of Effects with MediatorsJun 30 2019Suppose X and Y are binary exposure and outcome variables, and we have full knowledge of the distribution of Y, given application of X. From this we know the average causal effect of X on Y. We are now interested in assessing, for a case that was exposed ... More
Geodesic Distance Estimation with SphereletsJun 29 2019Many statistical and machine learning approaches rely on pairwise distances between data points. The choice of distance metric has a fundamental impact on performance of these procedures, raising questions about how to appropriately calculate distances. ... More
A New Lower Bound for Kullback-Leibler Divergence Based on Hammersley-Chapman-Robbins BoundJun 29 2019In this paper, we derive a useful lower bound for the Kullback-Leibler divergence (KL-divergence) based on the Hammersley-Chapman-Robbins bound (HCRB). The HCRB states that the variance of an estimator is bounded from below by the Chi-square divergence ... More
Multidimensional Scaling on Metric Measure SpacesJun 29 2019Multidimensional scaling (MDS) is a popular technique for mapping a finite metric space into a low-dimensional Euclidean space in a way that best preserves pairwise distances. We overview the theory of classical MDS, along with its optimality properties ... More
Statistical estimation of the Kullback-Leibler divergenceJun 29 2019Wide conditions are provided to guarantee asymptotic unbiasedness and L^2-consistency of the introduced estimates of the Kullback-Leibler divergence for probability measures in R^d having densities w.r.t. the Lebesgue measure. These estimates are constructed ... More
Large-scale inference with block structureJun 28 2019The detection of weak and rare effects in large amounts of data arises in a number of modern data analysis problems. Known results show that in this situation the potential of statistical inference is severely limited by the large-scale multiple testing ... More
Constrained Monte Carlo Markov Chains on GraphsJun 28 2019This paper presents a novel theoretical Monte Carlo Markov chain procedure in the framework of graphs. It specifically deals with the construction of a Markov chain whose empirical distribution converges to a given reference one. The Markov chain is constrained ... More
Robust test for dispersion parameter change in discretely observed diffusion processesJun 28 2019This paper deals with the problem of testing for dispersion parameter change in discretely observed diffusion processes when the observations are contaminated by outliers. To lessen the impact of outliers, we first calculate residuals using a robust estimate ... More
High-dimensional principal component analysis with heterogeneous missingnessJun 28 2019We study the problem of high-dimensional Principal Component Analysis (PCA) with missing observations. In simple, homogeneous missingness settings with a noise level of constant order, we show that an existing inverse-probability weighted (IPW) estimator ... More
The multidimensional truncated Moment Problem: Shape and Gaussian Mixture Reconstruction from Derivatives of MomentsJun 28 2019In this paper we introduce the theory of derivatives of moments and (moment) functionals to represent moment functionals by Gaussian mixtures, characteristic functions of polytopes, and simple functions of polytopes. We study, among other measures, Gaussian ... More
Multiple Testing and Variable Selection along Least Angle Regression's pathJun 28 2019In this article we investigate the outcomes of the standard Least Angle Regression (LAR) algorithm in high dimensions under the Gaussian noise assumption. We give the exact law of the sequence of knots conditional on the sequence of variables entering ... More
Differentially private sub-Gaussian location estimatorsJun 27 2019We tackle the problem of estimating a location parameter with differential privacy guarantees and sub-Gaussian deviations. Recent work in statistics has focused on the study of estimators that achieve sub-Gaussian type deviations even for heavy tailed ... More
Quality analysis in acyclic production networksJun 27 2019The production network under examination consists of a number of workstations. Each workstation is a parallel configuration of machines performing the same kind of tasks on a given part. Parts move from one workstation to another and at each workstation ... More
The exact form of the 'Ockham factor' in model selectionJun 27 2019We unify the Bayesian and Frequentist justifications for model selection based upon maximizing the evidence, using a precise definition of model complexity which we call 'flexibility'. In the Gaussian linear model, flexibility is asymptotically equal ... More
Quantum Entropy Scoring for Fast Robust Mean Estimation and Improved Outlier DetectionJun 26 2019We study two problems in high-dimensional robust statistics: \emph{robust mean estimation} and \emph{outlier detection}. In robust mean estimation the goal is to estimate the mean $\mu$ of a distribution on $\mathbb{R}^d$ given $n$ independent samples, ... More
Statistically and Computationally Efficient Change Point Localization in Regression SettingsJun 26 2019Detecting when the underlying distribution changes from the observed time series is a fundamental problem arising in a broad spectrum of applications. Change point localization is particularly challenging when we only observe low-dimensional projections ... More
Correlators of Polynomial ProcessesJun 26 2019A process is polynomial if its extended generator maps any polynomial to a polynomial of equal or lower degree. Then its conditional moments can be calculated in closed form, up to the computation of the exponential of the so-called generator matrix. ... More
Benign Overfitting in Linear RegressionJun 26 2019The phenomenon of benign overfitting is one of the key mysteries uncovered by deep learning methodology: deep neural networks seem to predict well, even with a perfect fit to noisy training data. Motivated by this phenomenon, we consider when a perfect ... More
Rerandomization and Regression AdjustmentJun 26 2019Randomization is a basis for the statistical inference of treatment effects without strong assumptions on the outcome-generating process. Appropriately using covariates further yields more precise estimators in randomized experiments. R. A. Fisher suggested ... More
Principal Component Analysis for Multivariate ExtremesJun 26 2019The first order behavior of multivariate heavy-tailed random vectors above large radial thresholds is ruled by a limit measure in a regular variation framework. For a high dimensional vector, a reasonable assumption is that the support of this measure ... More
Sampling of multiple variables based on partial order set theoryJun 26 2019This paper is going to introduce a new method for ranked set sampling with multiple criteria. The method is based on a version of ranked set sampling, introduced by Panahbehagh et al. (2017), which relaxes the restriction of selecting just one individual ... More
Preliminary test estimation in ULAN modelsJun 26 2019Preliminary test estimation, which is a natural procedure when it is suspected a priori that the parameter to be estimated might take value in a submodel of the model at hand, is a classical topic in estimation theory. In the present paper, we establish ... More
An urn model with local reinforcement: a theoretical framework for a chi-squared goodness of fit test with a big sampleJun 26 2019Motivated by recent studies of big samples, this work aims at constructing a parametric model which is characterized by the following features: (i) a "local" reinforcement, i.e. a reinforcement mechanism mainly based on the last observations, (ii) a random ... More
Upper tail dependence and smoothness of random fieldsJun 26 2019The modeling of risk situations that occur in a space-time framework can be done using max-stable random fields. Although the summary coefficients of the spatial and temporal dependence do not characterize the finite-dimensional distributions of the random ... More
Clustering piecewise stationary processesJun 26 2019The problem of time-series clustering is considered in the case where each data-point is a sample generated by a piecewise stationary ergodic process. Stationary processes are perhaps the most general class of processes considered in non-parametric statistics ... More
Control variate selection for Monte Carlo integrationJun 26 2019Monte Carlo integration with variance reduction by means of control variates can be implemented by the ordinary least squares estimator for the intercept in a multiple linear regression model with the integrand as response and the control variates as ... More
Piecewise polynomial approximation of probability density functions with application to uncertainty quantification for stochastic PDEsJun 26 2019The probability density function (PDF) associated with a given set of samples is approximated by a piecewise-linear polynomial constructed with respect to a binning of the sample space. The kernel functions are a compactly supported basis for the space ... More
On the definition of likelihood functionJun 25 2019We discuss a general definition of likelihood function in terms of Radon-Nikod\'{y}m derivatives. The definition is validated by the Likelihood Principle once we establish a result regarding the proportionality of likelihood functions under different ... More
AMF: Aggregated Mondrian Forests for Online LearningJun 25 2019Random Forests (RF) is one of the algorithms of choice in many supervised learning applications, be it classification or regression. The appeal of such methods comes from a combination of several characteristics: a remarkable accuracy in a variety of ... More