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James-Stein estimators for time series regression models

Author

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  • Senda, Motohiro
  • Taniguchi, Masanobu

Abstract

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.

Suggested Citation

  • Senda, Motohiro & Taniguchi, Masanobu, 2006. "James-Stein estimators for time series regression models," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 1984-1996, October.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:9:p:1984-1996
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    References listed on IDEAS

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    1. Masanobu Taniguchi & Junichi Hirukawa, 2005. "The Stein–James estimator for short- and long-memory Gaussian processes," Biometrika, Biometrika Trust, vol. 92(3), pages 737-746, September.
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    Cited by:

    1. Shiraishi, Hiroshi & Taniguchi, Masanobu & Yamashita, Takashi, 2018. "Higher-order asymptotic theory of shrinkage estimation for general statistical models," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 198-211.
    2. Xue, Yujie & Taniguchi, Masanobu & Liu, Tong, 2024. "Shrinkage estimators of BLUE for time series regression models," Journal of Multivariate Analysis, Elsevier, vol. 202(C).

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