On large deviation asymptotics of some tests in time series

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Abstract

Let {Xt} be a Gaussian stationary process with spectral density fθ(λ). The problem considered is that of testing a simple hypothesis H0:θ=θ0 against the alternative A:θ≠θ0. For this we investigate the Bahadur efficiency of the likelihood ratio, Rao, modified Wald and Wald tests. The Bahadur efficiency is based on the large deviation theory. Then it is shown that the asymptotics of the above tests are identical up to second-order in a certain sense. We show that this result makes a sharp contrast with the ordinary higher-order asymptotic theory for tests.

Original languageEnglish
Pages (from-to)191-200
Number of pages10
JournalJournal of Statistical Planning and Inference
Volume97
Issue number1
DOIs
Publication statusPublished - 2001 Aug 1
Externally publishedYes

Keywords

  • 60F10
  • 62F03
  • 62M10
  • Bahadur efficiency
  • Gaussian stationary process
  • Hypothesis testing
  • Large deviation
  • Spectral density

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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