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Nonparametric generalized likelihood ratio test is popularly used for modelchecking for regressions. However, there are two issues that may be thebarriers for its powerfulness. First, the bias term in its liming nulldistribution causes the test not to well control type I error and thus MonteCarlo approximation for critical value determination is required. Second, itseverely suffers from the curse of dimensionality due to the use ofmultivariate nonparametric function estimation. The purpose of this paper isthus two-fold: a bias-correction is suggested to this test and a dimensionreduction-based model-adaptive enhancement is recommended to promote the powerperformance. The proposed test still possesses the Wilks phenomenon, and thetest statistic can converge to its limit at a much faster rate and is much moresensitive to alternative models than the original nonparametric generalizedlikelihood ratio test as if the dimension of covariates were one. Simulationstudies are conducted to evaluate the finite sample performance and to comparewith other popularly used tests. A real data analysis is conducted forillustration.

Enhancements of nonparametric generalized likelihood ratio test: Bias-correction and dimension reduction