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Optimal testing in a class of nonregular models

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  • Yuya Shimizu
  • Taisuke Otsu

Abstract

This paper studies optimal hypothesis testing for nonregular statistical models with parameter-dependent support. We consider both one-sided and two-sided hypothesis testing and develop asymptotically uniformly most powerful tests based on the likelihood ratio process. The proposed one-sided test involves randomization to achieve asymptotic size control, some tuning constant to avoid discontinuities in the limiting likelihood ratio process, and a user-specified alternative hypothetical value to achieve the asymptotic optimality. Our two-sided test becomes asymptotically uniformly most powerful without imposing further restrictions such as unbiasedness. Simulation results illustrate desirable power properties of the proposed tests.

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  • Yuya Shimizu & Taisuke Otsu, 2024. "Optimal testing in a class of nonregular models," Papers 2403.16413, arXiv.org.
    • Handle: RePEc:arx:papers:2403.16413
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    File URL: http://arxiv.org/pdf/2403.16413
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