Acta mathematica scientia,Series A

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Additional Remarks on a Superiority Problem in Misspecified Re stricted Singular Linear Models

 ZHANG Bao-Xue   

  1. 北京理工大学应用数学系 北京 100081 复旦大学数学研究所 上海 200433
  • Online:2003-06-25 Published:2003-06-25
  • Supported by:

    国家自然科学基金数学天元青年基金资助项目(批准号:10226024);中国博士后科学基金资助项目(批准号:2002031180)和复旦大学数学所非线性科学重点实验室资助项目

Abstract:

When the covariance matrix of the disturbance vector in t he general linear model is misspecified, Gross, Trenkler and Liski (1998) showed  Razzaghi's (1987) result that sufficient condition for nonnegative definitness  of the covariance matrix difference of competing estimators is also necessary by  applying a result of Kabe and Gupta (1989). Further, Zhang and Liu (2000) exten ded the Theorem 1 of Gross, Trenkler and Liski to the singular linear model usin g matrix inequality and subspace relations. The aim of this paper is to prove th e conjecture which Razzaghi (1987) made is true in misspecified restricted singu lar linear model and strengthen Theorem 2 of Gross, Trenkler and Liski by giving  the necessary and sufficient conditions for nonnegative definiteness of the cov ariance matrix difference in the singular linear model.

Key words: Best linear unbiased estimator, Singular linear model, R estrictions, Covarinance matrix

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