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Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…

Probability · Mathematics 2021-11-25 Hansjoerg Albrecher , Martin Bladt , Mogens Bladt , Jorge Yslas

We consider the problem of estimating fold-changes in the expected value of a multivariate outcome observed with unknown sample-specific and category-specific perturbations. This challenge arises in high-throughput sequencing studies of the…

Methodology · Statistics 2026-04-24 David S Clausen , Sarah Teichman , Amy D Willis

The problem of change-point estimation is considered under a general framework where the data are generated by unknown stationary ergodic process distributions. In this context, the consistent estimation of the number of change-points is…

Machine Learning · Statistics 2013-02-15 Azaden Khaleghi , Daniil Ryabko

We analyse a multilevel Monte Carlo method for the approximation of distribution functions of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide an…

Probability · Mathematics 2017-06-22 Mike B. Giles , Tigran Nagapetyan , Klaus Ritter

Many functionals of interest in statistics and machine learning can be written as minimizers of expected loss functions. Such functionals are called $M$-estimands, and can be estimated by $M$-estimators -- minimizers of empirical average…

Statistics Theory · Mathematics 2024-11-27 Arunav Bhowmick , Arun Kumar Kuchibhotla

Motivated by the problem of dealing with incomplete or imprecise acquisition of data in computer vision and computer graphics, we extend results concerning the stability of persistent homology with respect to function perturbations to…

Algebraic Topology · Mathematics 2010-05-11 Patrizio Frosini , Claudia Landi

Estimation of the level set of a function (i.e., regions where the function exceeds some value) is an important problem with applications in digital elevation mapping, medical imaging, astronomy, etc. In many applications, the function of…

Applications · Statistics 2018-03-06 Kalyani Krishnamurthy , Waheed U. Bajwa , Rebecca Willett

We investigate the estimation of a weighted density taking the form $g=w(F)f$, where $f$ denotes an unknown density, $F$ the associated distribution function and $w$ is a known (non-negative) weight. Such a class encompasses many examples,…

Statistics Theory · Mathematics 2017-03-13 Fabien Navarro , Christophe Chesneau , Jalal Fadili

The problem of estimating the Kullback-Leibler divergence $D(P\|Q)$ between two unknown distributions $P$ and $Q$ is studied, under the assumption that the alphabet size $k$ of the distributions can scale to infinity. The estimation is…

Information Theory · Computer Science 2018-02-22 Yuheng Bu , Shaofeng Zou , Yingbin Liang , Venugopal V. Veeravalli

We extend some recent results on the Hausdorff convergence of level-sets for total variation regularized linear inverse problems. Dimensions higher than two and measurements in Banach spaces are considered. We investigate the relation…

Optimization and Control · Mathematics 2021-06-09 José A. Iglesias , Gwenael Mercier

Many statistical estimands can expressed as continuous linear functionals of a conditional expectation function. This includes the average treatment effect under unconfoundedness and generalizations for continuous-valued and personalized…

Methodology · Statistics 2020-11-23 David A. Hirshberg , Stefan Wager

The estimation of information measures of continuous distributions based on samples is a fundamental problem in statistics and machine learning. In this paper, we analyze estimates of differential entropy in $K$-dimensional Euclidean space,…

Information Theory · Computer Science 2021-11-29 Georg Pichler , Pablo Piantanida , Günther Koliander

In this article we investigate consistency of selection in regression models via the popular Lasso method. Here we depart from the traditional linear regression assumption and consider approximations of the regression function $f$ with…

Statistics Theory · Mathematics 2008-12-18 Florentina Bunea

This paper investigates the problem of testing independence of two random vectors of general dimensions. For this, we give for the first time a distribution-free consistent test. Our approach combines distance covariance with the…

Statistics Theory · Mathematics 2020-06-11 Hongjian Shi , Mathias Drton , Fang Han

This paper concerns the estimation of sums of functions of observable and unobservable variables. Lower bounds for the asymptotic variance and a convolution theorem are derived in general finite- and infinite-dimensional models. An explicit…

Statistics Theory · Mathematics 2007-06-13 Cun-Hui Zhang

We consider the problem of evaluating the cumulative distribution function (CDF) of the sum of order statistics, which serves to compute outage probability (OP) values at the output of generalized selection combining receivers. Generally,…

Computation · Statistics 2017-11-15 Nadhir Ben Rached , Zdravko Botev , Abla Kammoun , Mohamed-Slim Alouini , Raul Tempone

The level set estimation problem seeks to identify regions within a set of candidate points where an unknown and costly to evaluate function's value exceeds a specified threshold, providing an efficient alternative to exhaustive evaluations…

Machine Learning · Statistics 2025-03-27 Hideaki Ishibashi , Kota Matsui , Kentaro Kutsukake , Hideitsu Hino

We introduce a rank-statistic approximation of $f$-divergences that avoids explicit density-ratio estimation by working directly with the distribution of ranks. For a resolution parameter $K$, we map the mismatch between two univariate…

Machine Learning · Statistics 2026-02-02 Viktor Stein , José Manuel de Frutos

This paper examines the local linear regression (LLR) estimate of the conditional distribution function $F(y|x)$. We derive three uniform convergence results: the uniform bias expansion, the uniform convergence rate, and the uniform…

Econometrics · Economics 2023-06-07 Haitian Xie

The best-known and most commonly used distribution-property estimation technique uses a plug-in estimator, with empirical frequency replacing the underlying distribution. We present novel linear-time-computable estimators that significantly…

Statistics Theory · Mathematics 2019-03-06 Yi Hao , Alon Orlitsky