Validity of Edgeworth Expansions of Minimum Constrast Estimators for Gaussian ARMA Processes.

Abstract

Let (X sub t) be a Gaussian Autoregression Multivariant Analysis (ARMA) process with spectral density f sub p (lambda), where p is an unknown parameter. To estimate multivarant analysis we propose a minimum contrast estimation method which includes the maximum likelihood method and the quasi-maximum likelihood ethod as special cases. Let p-bar sub T be the minimum contrast estimator of p. Then we derive the Edgeworth expansion of the distribution of p-bar sub T up to third order, and provide its validity. 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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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1985
Accession Number
ADA169931

Entities

People

  • Masanobu Taniguchi

Organizations

  • University of Pittsburgh

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Asymptotic Series
  • Contrast
  • Data Science
  • Equations
  • Estimators
  • Governments
  • Information Science
  • Intellectual Property
  • Multivariate Analysis
  • Polynomials
  • Probability
  • Random Variables
  • Scientific Research
  • Stationary Processes
  • Two Dimensional
  • United States Government

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Statistical inference.