Open AccessA nondegenerate Vuong test and post selection confidence intervals for semi/nonparametric models
Author(s) -
Liao Zhipeng,
Shi Xiaoxia
Publication year - 2020
Publication title -
quantitative economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.062
H-Index - 27
eISSN - 1759-7331
pISSN - 1759-7323
DOI - 10.3982/qe1312
Subject(s) - mathematics , inference , nonparametric statistics , null hypothesis , model selection , parametric statistics , sample size determination , statistical hypothesis testing , selection (genetic algorithm) , monte carlo method , statistical inference , likelihood ratio test , statistics , computer science , artificial intelligence
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.