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.

翻译：本文研究参数依赖支撑的非正则统计模型中的最优假设检验。我们考虑单侧和双侧假设检验，并基于似然比过程发展渐近一致最优势检验。所提出的单侧检验涉及随机化以实现渐近尺度控制，引入调谐常数以避免极限似然比过程中的不连续性，并采用用户指定的备择假设值以实现渐近最优性。我们的双侧检验无需施加无偏性等额外约束即可成为渐近一致最优势检验。模拟结果显示所提检验具有理想的功效性质。