On the asymptotic behaviour of the pseudolikelihood ratio test statistic with boundary problems

Yong Chen, Kung Yee Liang

Research output: Contribution to journalArticlepeer-review


This paper considers the asymptotic distribution of the likelihood ratio statistic T for testing a subset of parameter of interest θ, θ = (γ, η) H0 γ = γo, based on the pseudolikelihood L(θ,φ) where φ is a consistent estimator of φ, the nuisance parameter. We show that the asymptotic distribution of T under H0 is a weighted sum of independent chi-squared variables. Some sufficient conditions are provided for the limiting distribution to be a chi-squared variable. When the true value of the parameter of interest θ0, or the true value of the nuisance parameter φ0, lies on the boundary of parameter space, the problem is shown to be asymptotically equivalent to the problem of testing the restricted mean of a multivariate normal distribution based on one observation from a multivariate normal distribution with misspecified covariance matrix, or from a mixture of multivariate normal distributions. A variety of examples are provided for which the limiting distributions of T may be mixtures of chi-squared variables. We conducted simulation studies to examine the performance of the likelihood ratio test statistics in variance component models and teratological experiments.

Original languageEnglish (US)
Pages (from-to)603-620
Number of pages18
Issue number3
StatePublished - Sep 1 2010


  • Asymptotic distribution
  • Boundary problem
  • Frailty survival model
  • Likelihood ratio test
  • Nuisance parameter
  • Pseudolikelihood
  • Teratological experiment
  • Variance component model

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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