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Preprint Sep 2026

SPARK: A General Goodness-of-Fit Assessment via Residual Projection

Goodness-of-fit testing is a basic tool for assessing whether a fitted procedure has captured the systematic information contained in the covariates. While traditional theory has largely focused on parametric regression models, modern data analysis increasingly relies on flexible black-box learners, whose predictive su...

Xing-Wei Liu, Yu-Hong Yang, Wang-Li Xu · 0 citations
Case report Open access Aug 2026

Regularized goodness-of-fit statistics and exact nonparametric confidence bands for distributions with application to household consumption

We study from a finite-sample viewpoint the problem of building tests and simultaneous confidence bands for cumulative distribution functions (CDFs), continuous or discrete. We emphasize procedures based on reweighted empirical distribution function (EDF) with shrinking bandwidths in the tails of the distribution. Sinc...

Jean-Marie Dufour, Mame Astou Diouf · 0 citations
Preprint Sep 2026

Goodness-of-fit for distributions on metric spaces

We propose a general goodness-of-fit framework for distributions on separable metric spaces. Under suitable identifiability conditions, probability distributions are characterized by distance profiles, which motivates their use in goodness-of-fit testing, for simple and composite null hypotheses. For composite null hyp...

Diego Serrano, Eduardo Garc'ia-Portugu'es, I. Van Keilegom · 0 citations
Preprint Sep 2026

Goodness-of-fit testing for the Pareto type-I distribution based on a mean residual life characterization

The statistical analysis of heavy-tailed data has received considerable attention because extreme observations frequently arise in many practical applications. The Pareto type-I distribution is a fundamental heavy-tailed model used in economics, finance, actuarial science, insurance, reliability, and extreme value anal...

S. Nila, Ishapathik Das, N. Balakrishna · 0 citations
Preprint Aug 2026

Goodness-of-Fit Tests and Calibration Machine-Learning Algorithms for Logistic Regression with Sparse Data

Assessing the goodness-of-fit of a logistic regression model is a critical prerequisite before the model is used for inference. However, goodness-of-fit (GOF) tests such as the chi-square and deviance tests often give invalid results when the data are"sparse"-- a common issue with continuous predictors like age or weig...

Ebrahim Khaled Ebrahim · 1 citation
Preprint Aug 2026

Distribution-free testing of linear type

We introduce a distribution-free goodness-of-fit test, termed the omega-1 test, which naturally complements the Kolmogorov--Smirnov test and Cram\'{e}r--von Mises test and can be viewed as their (piecewise) linear analog. Defined as an $\mathrm{L}^{1}$-functional of the empirical process, the test statistic improves on...

Wei-Xu Xia · 0 citations

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