PREDICTIVE ESTIMATION OF A COVARIANCE MATRIX AND ITS STRUCTURAL PARAMETERS

• Ogasawara Haruhiko

  Otaru University of Commerce

Abstract

Methods of estimating an unconstrained covariance matrix are derived using future data as well as current data in the likelihood. The estimators are obtained by optimizing coefficient(s) for adjusting the usual maximum likelihood estimators based on current data. The optimization is given by maximizing the expected log-likelihood over the distributions of future and current data. Under the Wishart and normal distributions,the coefficients in their adjusted estimators are obtained using known quantities. When a covariance matrix is structured with structural parameters, asymptotic adjustments of the Wishart maximum likelihood estimators are obtained. Similar estimators of an unconstrained covariance matrix derived by minimizing the mean square error are also given. Numerical illustrations with simulations are shown using factor analysis models. Methods of overcoming the problem of the dependence of the optimal values on unknown population values are discussed.

Journal

• Journal of the Japanese Society of Computational Statistics

  Journal of the Japanese Society of Computational Statistics 30 (1), 45-63, 2017

  Japanese Society of Computational Statistics

Keywords

• <i>Covariance structure</i>
• Factor analysis
• Predictive estimators
• Expected likelihood
• Mean square error
• Kullback-Leibler distance

Details

• CRID: 1390282679390543616
• NII Article ID: 130006602338
• NII Book ID: AA10823693
• DOI: 10.5183/jjscs.1706001_243
• ISSN: 18811337
• ISSN: 09152350
• NDL BIB ID: 030633058
• Web Site: http://id.ndl.go.jp/bib/030633058
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I030633058
• Web Site: https://www.jstage.jst.go.jp/article/jjscs/30/1/30_1706001_243/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed