A nondegenerate Vuong test and post selection confidence intervals for semi/nonparametric models

• 成果类型: Article
• 署名作者: Liao, Zhipeng; Shi, Xiaoxia
• 署名单位: University of California System; University of California Los Angeles; University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: QUANTITATIVE ECONOMICS
• ISSN/ISSBN: 1759-7323
• DOI: 10.3982/QE1312
• 发表日期: 2020
• 页码: 983-1017
• 关键词: Asymptotic size; model selection; comparison test; post model selection inference; semi; nonparametric models; C14; C31; C32

摘要

This paper proposes a new model selection test for the statistical comparison of semi/non-parametric models based on a general quasi-likelihood ratio criterion. An important feature of the new test is its uniformly exact asymptotic size in the overlapping nonnested case, as well as in the easier nested and strictly nonnested cases. The uniform size control is achieved without using pretesting, sample-splitting, or simulated critical values. We also show that the test has nontrivial power against all n-local alternatives and against some local alternatives that converge to the null faster than n. Finally, we provide a framework for conducting uniformly valid post model selection inference for model parameters. The finite sample performance of the nondegenerate test and that of the post model selection inference procedure are illustrated in a mean-regression example by Monte Carlo.