English
Related papers

Related papers: A Stein Goodness-of-fit Test for Directional Distr…

200 papers

We consider the approximation of the stationary distribution of the finite inclusion process with the Poisson-Dirichlet distribution. Using Stein's method, we derive an explicit bound for the approximation error, which is of order 1/N in…

Probability · Mathematics 2025-12-18 Han L. Gan

Nonparametric 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.…

Statistics Theory · Mathematics 2019-09-10 Tong Li , Ming Yuan

The coefficient of determination, known as $R^2$, is commonly used as a goodness-of-fit criterion for fitting linear models. $R^2$ is somewhat controversial when fitting nonlinear models, although it may be generalised on a case-by-case…

Methodology · Statistics 2021-12-23 Mark Levene , Aleksejus Kononovicius

In this paper we introduce a novel statistical framework based on the first two quantile conditional moments that facilitates effective goodness-of-fit testing for one-sided L\'evy distributions. The scale-ratio framework introduced in this…

Methodology · Statistics 2023-11-28 Kewin Pączek , Damian Jelito , Marcin Pitera , Agnieszka Wyłomańska

Distributional transformations characterized by equations relating expectations of test functions weighted by a given biasing function on the original distribution to expectations of the test function's higher derivatives with respect to…

Probability · Mathematics 2015-09-23 Christian Döbler

We consider spherical data $X_i$ noised by a random rotation $\varepsilon_i\in$ SO(3) so that only the sample $Z_i=\varepsilon_iX_i$, $i=1,\dots, N$ is observed. We define a nonparametric test procedure to distinguish $H_0:$ ''the density…

Statistics Theory · Mathematics 2013-11-18 Claire Lacour , Thanh Mai Pham Ngoc

A nonparametric kernel density estimator for directional-linear data is introduced. The proposal is based on a product kernel accounting for the different nature of both (directional and linear) components of the random vector. Expressions…

We investigate stability of invariant measures of diffusion processes with respect to $L^p$ distances on the coefficients, under an assumption of log-concavity. The method is a variant of a technique introduced by Crippa and De Lellis to…

Probability · Mathematics 2020-10-28 Max Fathi , Dan Mikulincer

We consider a linear regression model and propose an omnibus test to simultaneously check the assumption of independence between the error and the predictor variables, and the goodness-of-fit of the parametric model. Our approach is based…

Methodology · Statistics 2014-05-06 Arnab Sen , Bodhisattva Sen

We introduce a general framework for testing temporal symmetries in time series based on the distribution of ordinal patterns. While previous approaches have focused on specific forms of asymmetry, such as time reversal, our method provides…

Statistics Theory · Mathematics 2026-01-21 Annika Betken , Giorgio Micali , Manuel Ruiz Marín

We investigate the discrepancy principle for choosing smoothing parameters for kernel density estimation. The method is based on the distance between the empirical and estimated distribution functions. We prove some new positive and…

Statistics Theory · Mathematics 2015-03-19 Thoralf Mildenberger

The derivation and application of Stein identities have received considerable research interest in recent years, especially for continuous or discrete-univariate distributions. In this paper, we complement the existing literature by…

Methodology · Statistics 2026-03-02 Shaochen Wang , Christian H. Weiß

Exact null distributions of goodness-of-fit test statistics are generally challenging to obtain in tractable forms. Practitioners are therefore usually obliged to rely on asymptotic null distributions or Monte Carlo methods, either in the…

Methodology · Statistics 2023-09-06 Alberto Fernández-de-Marcos , Eduardo García-Portugués

This work builds a unified framework for the study of quadratic form distance measures as they are used in assessing the goodness of fit of models. Many important procedures have this structure, but the theory for these methods is dispersed…

Statistics Theory · Mathematics 2008-12-18 Bruce G. Lindsay , Marianthi Markatou , Surajit Ray , Ke Yang , Shu-Chuan Chen

Stein discrepancies (SDs) monitor convergence and non-convergence in approximate inference when exact integration and sampling are intractable. However, the computation of a Stein discrepancy can be prohibitive if the Stein operator - often…

Machine Learning · Statistics 2020-10-26 Jackson Gorham , Anant Raj , Lester Mackey

A large class of goodness-of-fit test statistics based on sup-functionals of weighted empirical processes is proposed and studied. The weight functions employed are Erd\H{o}s-Feller-Kolmogorov-Petrovski upper-class functions of a Brownian…

Statistics Theory · Mathematics 2016-04-04 Natalia Stepanova , Tatjana Pavlenko

Logistic regression is widely used to model the propensity score in the analysis of nonignorable missing data. However, goodness-of-fit testing for this propensity score model has received limited attention in the literature. In this paper,…

Methodology · Statistics 2026-04-24 Manli Cheng , Yangjianchen Xu , Qinglong Tian , Pengfei Li

It is well known that the approximate distribution of the usual test statistic of a goodness-of-fit test is chi-square, with degrees of freedom equal to the number of categories minus 1 (assuming that no parameters are to be estimated --…

Statistics Theory · Mathematics 2014-10-28 Kris Duszak , Jan Vrbik

Density-based directed distances -- particularly known as divergences -- between probability distributions are widely used in statistics as well as in the adjacent research fields of information theory, artificial intelligence and machine…

Statistics Theory · Mathematics 2022-03-03 Michel Broniatowski , Wolfgang Stummer

Learning a stationary diffusion amounts to estimating the parameters of a stochastic differential equation whose stationary distribution matches a target distribution. We build on the recently introduced kernel deviation from stationarity…

Machine Learning · Statistics 2026-01-30 Fabian Bleile , Sarah Lumpp , Mathias Drton