Enhancements of Non-parametric Generalized Likelihood Ratio Test: Bias Correction and Dimension Reduction

Cuizhen Niu, Xu Guo, Lixing Zhu*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)217-254
Number of pages38
JournalScandinavian Journal of Statistics
Issue number2
Early online date20 Sept 2017
Publication statusPublished - Jun 2018

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • bias correction
  • dimension reduction
  • model adaption
  • non-parametric generalized likelihood ratio
  • Wilks phenomenon


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