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Enhancements of Non‐parametric Generalized Likelihood Ratio Test: Bias Correction and Dimension Reduction
Author(s) -
Niu Cuizhen,
Guo Xu,
Zhu Lixing
Publication year - 2018
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12298
Subject(s) - mathematics , test statistic , likelihood ratio test , dimensionality reduction , statistics , covariate , parametric statistics , sufficient dimension reduction , curse of dimensionality , dimension (graph theory) , likelihood principle , sliced inverse regression , statistical hypothesis testing , econometrics , likelihood function , estimation theory , regression analysis , regression , computer science , combinatorics , artificial intelligence , quasi maximum likelihood
Non‐parametric generalized likelihood ratio test is a popular method of model checking for regressions. However, there are two issues that may be the barriers for its powerfulness: existing bias term and curse of dimensionality. The purpose of this paper is thus twofold: a bias reduction is suggested and a dimension reduction‐based adaptive‐to‐model enhancement is recommended to promote the power performance. The proposed test statistic still possesses the Wilks phenomenon and behaves like a test with only one covariate. Thus, it converges to its limit at a much faster rate and is much more sensitive to alternative models than the classical non‐parametric generalized likelihood ratio test. As a by‐product, we also prove that the bias‐corrected test is more efficient than the one without bias reduction in the sense that its asymptotic variance is smaller. Simulation studies and a real data analysis are conducted to evaluate of proposed tests.