A0674
Title: Enhancements of nonparametric generalized likelihood ratio test: Bias-reduction and dimension reduction
Authors: Cuizhen Niu - Beijing Normal University (China) [presenting]
Xu Guo - Beijing Normal University (China)
Lixing Zhu - Beijing Normal University (China)
Abstract: Nonparametric 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. First, the bias term in its limiting 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 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 nonparametric generalized likelihood ratio test. As a by-product, we also prove that the bias-corrected test can be more efficient than the one without bias-reduction in the sense that its asymptotic variance is smaller. 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.
