James-Stein estimators for time series regression models

Motohiro Senda, Masanobu Taniguchi*


研究成果: Article査読

5 被引用数 (Scopus)


The least squares (LS) estimator seems the natural estimator of the coefficients of a Gaussian linear regression model. However, if the dimension of the vector of coefficients is greater than 2 and the residuals are independent and identically distributed, this conventional estimator is not admissible. James and Stein [Estimation with quadratic loss, Proceedings of the Fourth Berkely Symposium vol. 1, 1961, pp. 361-379] proposed a shrinkage estimator (James-Stein estimator) which improves the least squares estimator with respect to the mean squares error loss function. In this paper, we investigate the mean squares error of the James-Stein (JS) estimator for the regression coefficients when the residuals are generated from a Gaussian stationary process. Then, sufficient conditions for the JS to improve the LS are given. It is important to know the influence of the dependence on the JS. Also numerical studies illuminate some interesting features of the improvement. The results have potential applications to economics, engineering, and natural sciences.

ジャーナルJournal of Multivariate Analysis
出版ステータスPublished - 2006 10月

ASJC Scopus subject areas

  • 統計学および確率
  • 数値解析
  • 統計学、確率および不確実性


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