James-Stein estimators for time series regression models

Motohiro Senda, Masanobu Taniguchi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (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.

Original languageEnglish
Pages (from-to)1984-1996
Number of pages13
JournalJournal of Multivariate Analysis
Issue number9
Publication statusPublished - 2006 Oct
Externally publishedYes


  • Gaussian stationary process
  • James-Stein estimator
  • Least squares estimator
  • Mean squares error
  • Regression spectrum
  • Residual spectral density matrix
  • Time series regression model

ASJC Scopus subject areas

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


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