English
Related papers

Related papers: Testing normality via a distributional fixed point…

200 papers

We propose new affine invariant tests for multivariate normality, based on independence characterizations of the sample moments of the normal distribution. The test statistics are obtained using canonical correlations between sets of sample…

Methodology · Statistics 2015-03-11 Måns Thulin

We study sequences of scaled edge-corrected empirical (generalized) K-functions (modifying Ripley's K-function) each of them constructed from a single observation of a $d$-dimensional fourth-order stationary point process in a sampling…

Statistics Theory · Mathematics 2017-06-06 Lothar Heinrich

Goodness-of-fit testing is often criticized for its lack of practical relevance: since ``all models are wrong'', the null hypothesis that the data conform to our model is ultimately always rejected as the sample size grows. Despite this,…

Machine Learning · Statistics 2025-10-24 Xing Liu , François-Xavier Briol

The stochastic block model is a popular tool for studying community structures in network data. We develop a goodness-of-fit test for the stochastic block model. The test statistic is based on the largest singular value of a residual matrix…

Statistics Theory · Mathematics 2016-01-22 Jing Lei

The L\'evy distribution, alongside the Normal and Cauchy distributions, is one of the only three stable distributions whose density can be obtained in a closed form. However, there are only a few specific goodness-of-fit tests for the…

Methodology · Statistics 2023-08-02 Žikica Lukić , Bojana Milošević

Over the last 80 years there has been much interest in the problem of finding an explicit formula for the probability density function of two zero mean correlated normal random variables. Motivated by this historical interest, we use a…

Statistics Theory · Mathematics 2021-04-13 Robert E. Gaunt

This article gives a synopsis on new developments in affine invariant tests for multivariate normality in an i.i.d.-setting, with special emphasis on asymptotic properties of several classes of weighted $L^2$-statistics. Since weighted…

Statistics Theory · Mathematics 2020-04-17 Bruno Ebner , Norbert Henze

We consider two division models for structured cell populations, where cells can grow, age and divide. These models have been introduced in the literature under the denomination of `mitosis' and `adder' models. In the recent years, there…

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

A natural (yet unconventional) test for goodness-of-fit measures the discrepancy between the model and empirical distributions via their Euclidean distance (or, equivalently, via its square). The present paper characterizes the statistical…

Computation · Statistics 2012-06-28 William Perkins , Gary Simon , Mark Tygert

We present a novel data-oriented statistical framework that assesses the presumed Gaussian dependence structure in a pairwise setting. This refers to both multivariate normality and normal copula goodness-of-fit testing. The proposed test…

Methodology · Statistics 2024-04-23 Jakub Woźny , Piotr Jaworski , Damian Jelito , Marcin Pitera , Agnieszka Wyłomańska

We consider the goodness of fit testing problem for ergodic diffusion processes. The basic hypothesis is supposed to be simple. The diffusion coefficient is known and the alternatives are described by the different trend coefficients. We…

Statistics Theory · Mathematics 2009-03-27 Yury A. Kutoyants

We propose a goodness-of-fit measure for probability densities modeling observations with varying dimensionality, such as text documents of differing lengths or variable-length sequences. The proposed measure is an instance of the kernel…

Machine Learning · Statistics 2023-07-14 Jerome Baum , Heishiro Kanagawa , Arthur Gretton

Ordinal categorical data are widely collected in psychology, education, and other social sciences, appearing commonly in questionnaires, assessments, and surveys. Latent class models provide a flexible framework for uncovering unobserved…

Machine Learning · Statistics 2026-02-26 Huan Qing

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

We study the problem of learning fair prediction models for unseen test sets distributed differently from the train set. Stability against changes in data distribution is an important mandate for responsible deployment of models. The domain…

Machine Learning · Computer Science 2021-01-26 Harvineet Singh , Rina Singh , Vishwali Mhasawade , Rumi Chunara

We propose a class of nonparametric two-sample tests with a cost linear in the sample size. Two tests are given, both based on an ensemble of distances between analytic functions representing each of the distributions. The first test uses…

Machine Learning · Statistics 2015-06-16 Kacper Chwialkowski , Aaditya Ramdas , Dino Sejdinovic , Arthur Gretton

This paper considers the problem of testing the equality of two unspecified distributions. The classical omnibus tests such as the Kolmogorov-Smirnov and Cram\`er-von Mises are known to suffer from low power against essentially all but…

Statistics Theory · Mathematics 2015-09-15 Wen-Xin Zhou , Chao Zheng , Zhen Zhang

In this paper we are interested in testing whether there are any signals hidden in high dimensional noise data. Therefore we study the family of goodness-of-fit tests based on $\Phi$-divergences including the test of Berk and Jones as well…

Statistics Theory · Mathematics 2018-03-20 Marc Ditzhaus

Non-parametric goodness-of-fit testing procedures based on kernel Stein discrepancies (KSD) are promising approaches to validate general unnormalised distributions in various scenarios. Existing works focused on studying kernel choices to…

Methodology · Statistics 2022-06-02 Wenkai Xu