English
Related papers

Related papers: Central limit theorems for directional and linear …

200 papers

There is an increasing interest in algorithms to learn invariant correlations across training environments. A big share of the current proposals find theoretical support in the causality literature but, how useful are they in practice? The…

Machine Learning · Computer Science 2021-02-23 Benjamin Aubin , Agnieszka Słowik , Martin Arjovsky , Leon Bottou , David Lopez-Paz

In this paper we study goodness-of-fit testing of single-index models. The large sample behavior of certain score-type test statistics is investigated. As a by-product, we obtain asymptotically distribution-free maximin tests for a large…

Statistics Theory · Mathematics 2007-06-13 Winfried Stute , Li-Xing Zhu

The object of study is the problem of testing for uniformity of the multinomial distribution. We consider tests based on symmetric statistics, defined as the sum of some function of cell-frequencies. Mainly, attention is focused on the…

Statistics Theory · Mathematics 2022-09-12 Sherzod M. Mirakhmedov

In a previous article, a least square regression estimation procedure was proposed: first, we condiser a family of functions and study the properties of an estimator in every unidimensionnal model defined by one of these functions; we then…

Statistics Theory · Mathematics 2007-06-13 Pierre Alquier

The paper establishes the central limit theorems and proposes how to perform valid inference in factor models. We consider a setting where many counties/regions/assets are observed for many time periods, and when estimation of a global…

Econometrics · Economics 2023-06-22 Stanislav Anatolyev , Anna Mikusheva

We establish sufficient conditions for the asymptotic normality of kernel density estimators, applied to causal linear random fields. Our conditions on the coefficients of linear random fields are weaker than known results, although our…

Statistics Theory · Mathematics 2012-01-04 Yizao Wang , Michael Woodroofe

Limit theorems are proved for quadratic forms of Gaussian random fields in presence of long memory. We obtain a non central limit theorem under a minimal integrability condition, which allows isotropic and anisotropic models. We apply our…

Statistics Theory · Mathematics 2010-01-08 Frédéric Lavancier , Anne Philippe

We develop a central limit theorem (CLT) for a non-parametric estimator of the transition matrices in controlled Markov chains (CMCs) with finite state-action spaces. Our results establish precise conditions on the logging policy under…

Statistics Theory · Mathematics 2026-03-26 Ziwei Su , Imon Banerjee , Diego Klabjan

In this paper we prove a central limit theorem for some probability measures defined as asymtotic densities of integer sets defined via sum-of-digit-function. To any integer a we can associate a measure on Z called $\mu$a such that, for any…

Probability · Mathematics 2019-04-22 Jordan Emme , Pascal Hubert

We consider a nonparametric goodness of fit test problem for the drift coefficient of one-dimensional small diffusions. Our test is based on discrete observation of the processes, and the diffusion coefficient is a nuisance function which…

Statistics Theory · Mathematics 2008-01-29 Ilia Negri , Yoichi Nishiyama

A central limit theorem for arrays of symmetric row-wise exchangeable random variables is presented. The result is valid for finite and infinite extendable and non-extendable sequences. Unlike most reported versions of the central limit…

Probability · Mathematics 2020-06-22 Ilya Soloveychik

In this paper we consider the uniformity testing problem for high-dimensional discrete distributions (multinomials) under sparse alternatives. More precisely, we derive sharp detection thresholds for testing, based on $n$ samples, whether a…

Statistics Theory · Mathematics 2022-02-17 Bhaswar B. Bhattacharya , Rajarshi Mukherjee

This paper develops the process of using Richardson Extrapolation to improve the Kernel Density Estimation method, resulting in a more accurate (lower Mean Squared Error) estimate of a probability density function for a distribution of data…

Probability · Mathematics 2018-12-21 Ruben G. Ascoli

We present a limit theorem describing the behavior of a probabilistic model for square-free numbers. The limiting distribution has a density that comes from the Dickman-De Bruijn function and is constant on the interval $[0,1]$. We also…

Probability · Mathematics 2010-10-18 Francesco Cellarosi , Yakov G. Sinai

This paper develops a conditional independence (CI) test from a conditional density ratio (CDR) for weakly dependent data. The main contribution is presenting a closed-form expression for the estimated conditional density ratio function…

Methodology · Statistics 2025-04-25 Chunrong Ai , Zixuan Xu , Zheng Zhang

Motivated by applications to the study of depth functions for tree-indexed random variables generated by point processes, we describe functional limit theorems for the intensity measure of point processes. Specifically, we establish uniform…

Probability · Mathematics 2024-02-08 Giacomo Francisci , Anand N. Vidyashankar

New bandwidth selectors for kernel density estimation with directional data are presented in this work. These selectors are based on asymptotic and exact error expressions for the kernel density estimator combined with mixtures of von Mises…

Methodology · Statistics 2020-09-22 Eduardo García-Portugués

This paper discusses two goodness-of-fit testing problems. The first problem pertains to fitting an error distribution to an assumed nonlinear parametric regression model, while the second pertains to fitting a parametric regression model…

Statistics Theory · Mathematics 2007-06-13 Estate V. Khmaladze , Hira L. Koul

We survey some geometrical properties of trajectories of $d$-dimensional random walks via the application of functional limit theorems. We focus on the functional law of large numbers and functional central limit theorem (Donsker's…

Probability · Mathematics 2018-10-16 Chak Hei Lo , James McRedmond , Clare Wallace

We consider goodness-of-fit tests of symmetric stable distributions based on weighted integrals of the squared distance between the empirical characteristic function of the standardized data and the characteristic function of the standard…

Statistics Theory · Mathematics 2009-01-06 Muneya Matsui , Akimichi Takemura