Validity of Edgeworth expansions of minimum contrast estimators for Gaussian ARMA processes

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11 Citations (Scopus)

Abstract

Let {Xt} be a Gaussian ARMA process with spectral density fθ(λ), where θ is an unknown parameter. To estimate θ we propose a minimum contrast estimation method which includes the maximum likelihood method and the quasi-maximum likelihood method as special cases. Let θ̂τ be the minimum contrast estimator of θ. Then we derive the Edgewroth expansion of the distribution of θ̂τ up to third order, and prove its valldity. By this Edgeworth expansion we can see that this minimum contrast estimator is always second-order asymptotically efficient in the class of second-order asymptotically median unbiased estimators. Also the third-order asymptotic comparisons among minimum contrast estimators will be discussed.

Original languageEnglish
Pages (from-to)1-28
Number of pages28
JournalJournal of Multivariate Analysis
Volume21
Issue number1
DOIs
Publication statusPublished - 1987
Externally publishedYes

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Minimum Contrast Estimators
ARMA Process
Edgeworth Expansion
Gaussian Process
Maximum likelihood
Maximum Likelihood Method
Spectral density
Quasi-maximum Likelihood
Unbiased estimator
Spectral Density
Unknown Parameters
Estimate
Edgeworth expansion
Estimator
ARMA process

Keywords

  • Edgeworth expansion
  • Gaussian ARMA processes
  • maximum likelihood estimator
  • minimum contrast estimator

ASJC Scopus subject areas

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

Cite this

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abstract = "Let {Xt} be a Gaussian ARMA process with spectral density fθ(λ), where θ is an unknown parameter. To estimate θ we propose a minimum contrast estimation method which includes the maximum likelihood method and the quasi-maximum likelihood method as special cases. Let θ̂τ be the minimum contrast estimator of θ. Then we derive the Edgewroth expansion of the distribution of θ̂τ up to third order, and prove its valldity. By this Edgeworth expansion we can see that this minimum contrast estimator is always second-order asymptotically efficient in the class of second-order asymptotically median unbiased estimators. Also the third-order asymptotic comparisons among minimum contrast estimators will be discussed.",
keywords = "Edgeworth expansion, Gaussian ARMA processes, maximum likelihood estimator, minimum contrast estimator",
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AU - Taniguchi, Masanobu

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AB - Let {Xt} be a Gaussian ARMA process with spectral density fθ(λ), where θ is an unknown parameter. To estimate θ we propose a minimum contrast estimation method which includes the maximum likelihood method and the quasi-maximum likelihood method as special cases. Let θ̂τ be the minimum contrast estimator of θ. Then we derive the Edgewroth expansion of the distribution of θ̂τ up to third order, and prove its valldity. By this Edgeworth expansion we can see that this minimum contrast estimator is always second-order asymptotically efficient in the class of second-order asymptotically median unbiased estimators. Also the third-order asymptotic comparisons among minimum contrast estimators will be discussed.

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KW - maximum likelihood estimator

KW - minimum contrast estimator

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