Third order asymptotic properties of maximum likelihood estimators for Gaussian ARMA processes

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23 Citations (Scopus)

Abstract

In this paper we investigate various third-order asymptotic properties of maximum likelihood estimators for Gaussian ARMA processes by the third-order Edgeworth expansions of the sampling distributions. We define a third-order asymptotic efficiency by the highest probability concentration around the true value with respect to the third-order Edgeworth expansion. Then we show that the maximum likelihood estimator is not always third-order asymptotically efficient in the class A3 of third-order asymptotically median unbiased estimators. But, if we confine our discussions to an appropriate class D (⊂ A3) of estimators, we can show that appropriately modified maximum likelihood estimator is always third-order asymptotically efficient in D.

Original languageEnglish
Pages (from-to)1-31
Number of pages31
JournalJournal of Multivariate Analysis
Volume18
Issue number1
DOIs
Publication statusPublished - 1986 Feb
Externally publishedYes

Keywords

  • Edgeworth expansion
  • Gaussian autoregressive moving average processes
  • Toeplitz matrix
  • maximum likelihood estimator
  • residue theorem
  • spectral density
  • third order asymptotic efficiency

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

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