Distribution free MMD tests for model selection with estimated parameters

2023/05/12 by Florian Brück, Brück, Florian, Jean‐David Fermanian +3 · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Distribution Estimation and Applications #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2305.07549

openalex publication_date 2023/05/12 · openalex created_date 2023/05/18 · openalex updated_date 2026/07/28

Abstract

There exist some testing procedures based on the maximum mean discrepancy (MMD) to address the challenge of model specification. However, they ignore the presence of estimated parameters in the case of composite null hypotheses. In this paper, we first illustrate the effect of parameter estimation in model specification tests based on the MMD. Second, we propose simple model specification and model selection tests in the case of models with estimated parameters. All our tests are asymptotically standard normal under the null, even when the true underlying distribution belongs to the competing parametric families. A simulation study and a real data analysis illustrate the performance of our tests in terms of power and level.

Cited by

• Composite goodness-of-fit test with the Kernel Stein Discrepancy and a bootstrap for degenerate U-statistics with estimated parameters

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