English
Related papers

Related papers: Composite Goodness-of-fit Tests with Kernels

200 papers

Goodness-of-fit tests based on the empirical Wasserstein distance are proposed for simple and composite null hypotheses involving general multivariate distributions. For group families, the procedure is to be implemented after preliminary…

Methodology · Statistics 2021-01-28 Marc Hallin , Gilles Mordant , Johan Segers

We propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process. The empirical likelihood is used to formulate a statistic, for each kernel smoothing…

Statistics Theory · Mathematics 2009-09-29 Song Xi Chen , Jiti Gao , Cheng Yong Tang

Any applied mathematical model contains parameters. The paper proposes to use kernel learning for the parametric analysis of the model. The approach consists in setting a distribution on the parameter space, obtaining a finite training…

Optimization and Control · Mathematics 2025-01-27 Vladimir Norkin , Alois Pichler

It has recently been shown that an unbinned distance-based statistic, the energy, can be used to construct an extremely powerful nonparametric multivariate two sample goodness-of-fit test. An extension to this method that makes it possible…

Data Analysis, Statistics and Probability · Physics 2011-10-11 Mike Williams

Kernel means are frequently used to represent probability distributions in machine learning problems. In particular, the well known kernel density estimator and the kernel mean embedding both have the form of a kernel mean. Unfortunately,…

Machine Learning · Statistics 2015-03-03 E. Cruz Cortés , C. Scott

We study goodness-of-fit of discrete distributions in the distributed setting, where samples are divided between multiple users who can only release a limited amount of information about their samples due to various information constraints.…

Data Structures and Algorithms · Computer Science 2019-07-23 Jayadev Acharya , Clément L. Canonne , Yanjun Han , Ziteng Sun , Himanshu Tyagi

This paper presents and examines computationally convenient goodness-of-fit tests for the family of generalized Poisson distributions, which encompasses notable distributions such as the Compound Poisson and the Katz distributions. The…

Methodology · Statistics 2024-11-21 A. Batsidis , B. Milošević , M. D. Jiménez-Gamero

We consider the error distribution in functional linear models with scalar response and functional covariate. Different asymptotic expansions of the empirical distribution function and the empirical characteristic function based on…

Methodology · Statistics 2025-12-01 Natalie Neumeyer , Leonie Selk

We consider the goodness-of-fit testing problem of distinguishing whether the data are drawn from a specified distribution, versus a composite alternative separated from the null in the total variation metric. In the discrete case, we…

Statistics Theory · Mathematics 2017-07-03 Sivaraman Balakrishnan , Larry Wasserman

Much of machine learning relies on comparing distributions with discrepancy measures. Stein's method creates discrepancy measures between two distributions that require only the unnormalized density of one and samples from the other. Stein…

Machine Learning · Statistics 2020-07-21 Raghav Singhal , Xintian Han , Saad Lahlou , Rajesh Ranganath

This paper considers a class of nonparametric autoregressive models with nonstationarity. We propose a nonparametric kernel test for the conditional mean and then establish an asymptotic distribution of the proposed test. Both the setting…

Statistics Theory · Mathematics 2009-11-20 Jiti Gao , Maxwell King , Zudi Lu , Dag Tjøstheim

The field of causal discovery develops model selection methods to infer cause-effect relations among a set of random variables. For this purpose, different modelling assumptions have been proposed to render cause-effect relations…

Methodology · Statistics 2023-11-09 Daniela Schkoda , Mathias Drton

Statistical modeling plays a fundamental role in understanding the underlying mechanism of massive data (statistical inference) and predicting the future (statistical prediction). Although all models are wrong, researchers try their best to…

Methodology · Statistics 2020-06-17 Hangjin Jiang

This paper considers extensions of minimum-disparity estimators to the problem of estimating parameters in a regression model that is conditionally specified; that is where a parametric model describes the distribution of a response $y$…

Statistics Theory · Mathematics 2016-02-10 Giles Hooker

We propose two families of tests for the classical goodness-of-fit problem to univariate normality. The new procedures are based on $L^2$-distances of the empirical zero-bias transformation to the normal distribution or the empirical…

Methodology · Statistics 2020-02-25 Steffen Betsch , Bruno Ebner

Nonlinear kernels can be approximated using finite-dimensional feature maps for efficient risk minimization. Due to the inherent trade-off between the dimension of the (mapped) feature space and the approximation accuracy, the key problem…

Machine Learning · Computer Science 2018-10-10 Shahin Shahrampour , Vahid Tarokh

We propose and study a general method for construction of consistent statistical tests on the basis of possibly indirect, corrupted, or partially available observations. The class of tests devised in the paper contains Neyman's smooth…

Statistics Theory · Mathematics 2017-09-22 Mikhail Langovoy

Spherical and hyperspherical data are commonly encountered in diverse applied research domains, underscoring the vital task of assessing independence within such data structures. In this context, we investigate the properties of test…

Methodology · Statistics 2024-01-23 Marija Cuparić , Bruno Ebner , Bojana Milošević

The accurate representation of epistemic uncertainty is a challenging yet essential task in machine learning. A widely used representation corresponds to convex sets of probabilistic predictors, also known as credal sets. One popular way of…

Machine Learning · Computer Science 2025-07-30 Mira Jürgens , Thomas Mortier , Eyke Hüllermeier , Viktor Bengs , Willem Waegeman

Kernel-based testing has revolutionized the field of non-parametric tests through the embedding of distributions in an RKHS. This strategy has proven to be powerful and flexible, yet its applicability has been limited to the standard…

Methodology · Statistics 2024-11-28 Anthony Ozier-Lafontaine , Polina Arsenteva , Franck Picard , Bertrand Michel