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In this work, the distributional properties of the goodness-of-fit term in likelihood-based information criteria are explored. These properties are then leveraged to construct a novel goodness-of-fit test for normal linear regression models…

Methodology · Statistics 2023-09-20 Scott H. Koeneman , Joseph E. Cavanaugh

For ill-posed inverse problems, a regularised solution can be interpreted as a mode of the posterior distribution in a Bayesian framework. This framework enriches the set the solutions, as other posterior estimates can be used as a solution…

Statistics Theory · Mathematics 2013-04-22 Natalia Bochkina

We consider the problem of the construction of the goodness-of-fit tests for diffusion processes with small noise. The basic hypothesis is composite parametric and our goal is to obtain asymptotically distribution free tests. We propose two…

Statistics Theory · Mathematics 2015-09-30 Yury A. Kutoyants

A goodness-of-fit test for one-parameter count distributions with finite second moment is proposed. The test statistic is derived from the $L^1$ distance of a function of the probability generating function of the model under the null…

Statistics Theory · Mathematics 2024-06-11 Antonio Di Noia , Lucio Barabesi , Marzia Marcheselli , Caterina Pisani , Luca Pratelli

We propose a new class of goodness-of-fit tests for the inverse Gaussian distribution. The proposed tests are weighted $L^2$-type tests depending on a tuning parameter. We develop the asymptotic theory under the null hypothesis and under a…

Methodology · Statistics 2022-01-31 J. S. Allison , S. Betsch , B. Ebner , I. J. H. Visagie

This paper introduces a novel goodness-of-fit test technique for parametric conditional distributions. The proposed tests are based on a residual marked empirical process, for which we develop a conditional Principal Component Analysis. The…

Econometrics · Economics 2025-06-18 Cui Rui , Li Yuhao

Goodness-of-fit tests are often used in data analysis to test the agreement of a distribution to a set of data. These tests can be used to detect an unknown signal against a known background or to set limits on a proposed signal…

Methodology · Statistics 2023-03-20 Lolian Shtembari , Allen Caldwell

The objective of goodness-of-fit testing is to assess whether a dataset of observations is likely to have been drawn from a candidate probability distribution. This paper presents a rank-based family of goodness-of-fit tests that is…

Statistics Theory · Mathematics 2019-04-18 Feras A. Saad , Cameron E. Freer , Nathanael L. Ackerman , Vikash K. Mansinghka

We develop a general theory for the goodness-of-fit test to non-linear models. In particular, we assume that the observations are noisy samples of a submanifold defined by a \yao{sufficiently smooth non-linear map}. The observation noise is…

Machine Learning · Statistics 2020-11-12 Alexander Shapiro , Yao Xie , Rui Zhang

In the Bayesian approach, the a priori knowledge about the input of a mathematical model is described via a probability measure. The joint distribution of the unknown input and the data is then conditioned, using Bayes' formula, giving rise…

Statistics Theory · Mathematics 2015-06-15 Sebastian J. Vollmer

We develop a systematic, omnibus approach to goodness-of-fit testing for parametric distributional models when the variable of interest is only partially observed due to censoring and/or truncation. In many such designs, tests based on the…

Methodology · Statistics 2026-02-10 Juan Carlos Escanciano , Jacobo de Uña-Álvarez

We consider the nonparametric regression problem with multiple predictors and an additive error, where the regression function is assumed to be coordinatewise nondecreasing. We propose a Bayesian approach to make an inference on the…

Statistics Theory · Mathematics 2022-11-24 Kang Wang , Subhashis Ghosal

Motivated by applications to goodness of fit testing, the empirical likelihood approach is generalized to allow for the number of constraints to grow with the sample size and for the constraints to use estimated criteria functions. The…

Statistics Theory · Mathematics 2013-07-24 Hanxiang Peng , Anton Schick

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

Shape restrictions such as monotonicity on functions often arise naturally in statistical modeling. We consider a Bayesian approach to the problem of estimation of a monotone regression function and testing for monotonicity. We construct a…

Statistics Theory · Mathematics 2020-08-05 Moumita Chakraborty , Subhashis Ghosal

We consider the goodness of fit testing problem for stochastic differential equation with small diffiusion coefficient. The basic hypothesis is always simple and it is described by the known trend coefficient. We propose several tests of…

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

This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information…

Statistics Theory · Mathematics 2010-01-13 Yuan Liao , Wenxin Jiang

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

In this article, we study the binary classification problem with supervised data, in the case where the covariate-to-probability-of-success map is possibly spatially inhomogeneous. We devise nonparametric Bayesian procedures with…

Statistics Theory · Mathematics 2025-09-10 Matteo Giordano

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