Skip to main content
Article
On Likelihood Ratio Tests When Nuisance Parameters are Present Only Under the Alternative
Statistical Science (2014)
  • CZ Di, Fred Hutchinson Cancer Research Center
  • K-Y Liang, Johns Hopkins University
Abstract
In parametric models, when one or more parameters disappear under the null hypothesis, the likelihood ratio test statistic does not converge to chi-square distributions. Rather, its limiting distribution is shown to be equivalent to that of the supremum of a squared Gaussian process. However, the limiting distribution is analytically intractable for most of examples, and approximation or simulation based methods must be used to calculate the p values. In this article, we investigate conditions under which the asymptotic distributions have analytically tractable forms, based on the principal component decomposition of Gaussian processes. When these conditions are not satisfied, the principal component representation also motivates a simple and speedy simulation algorithm to approximate p values. The results are illustrated by Anderson’s stereotype model for ordinal data.
Keywords
  • Likelihood ratio test,
  • nonidentifiability,
  • Gaussian process,
  • principal component analysis
Publication Date
2014
Citation Information
CZ Di and K-Y Liang. "On Likelihood Ratio Tests When Nuisance Parameters are Present Only Under the Alternative" Statistical Science (2014)
Available at: http://works.bepress.com/di/8/