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

TL;DR

This paper improves the nonparametric generalized likelihood ratio test by introducing bias correction and dimension reduction techniques, enhancing its accuracy and power in model checking for regressions.

Contribution

It proposes a bias-correction method and a dimension reduction enhancement, making the test more reliable and powerful, especially in high-dimensional settings.

Findings

Bias correction reduces type I error control issues.

Dimension reduction improves test sensitivity and power.

Simulation studies confirm improved finite sample performance.

Abstract

Nonparametric generalized likelihood ratio test is popularly used for model checking for regressions. However, there are two issues that may be the barriers for its powerfulness. First, the bias term in its liming null distribution causes the test not to well control type I error and thus Monte Carlo approximation for critical value determination is required. Second, it severely suffers from the curse of dimensionality due to the use of multivariate nonparametric function estimation. The purpose of this paper is thus two-fold: a bias-correction is suggested to this test and a dimension reduction-based model-adaptive enhancement is recommended to promote the power performance. The proposed test still possesses the Wilks phenomenon, and the test statistic can converge to its limit at a much faster rate and is much more sensitive to alternative models than the original nonparametric generalized likelihood ratio test as if the dimension of covariates were one. Simulation studies are conducted to evaluate the finite sample performance and to compare with other popularly used tests. A real data analysis is conducted for illustration.