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Shrinkage estimators of BLUE for time series regression models

Author

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  • Xue, Yujie
  • Taniguchi, Masanobu
  • Liu, Tong

Abstract

The least squares estimator (LSE) seems a natural estimator of linear regression models. Whereas, if the dimension of the vector of regression coefficients is greater than 1 and the residuals are dependent, the best linear unbiased estimator (BLUE), which includes the information of the covariance matrix Γ of residual process has a better performance than LSE in the sense of mean square error. As we know the unbiased estimators are generally inadmissible, Senda and Taniguchi (2006) introduced a James–Stein type shrinkage estimator for the regression coefficients based on LSE, where the residual process is a Gaussian stationary process, and provides sufficient conditions such that the James–Stein type shrinkage estimator improves LSE. In this paper, we propose a shrinkage estimator based on BLUE. Sufficient conditions for this shrinkage estimator to improve BLUE are also given. Furthermore, since Γ is infeasible, assuming that Γ has a form of Γ=Γ(θ), we introduce a feasible version of that shrinkage estimator with replacing Γ(θ) by Γ(θˆ) which is introduced in Toyooka (1986). Additionally, we give the sufficient conditions where the feasible version improves BLUE. Besides, the results of a numerical studies confirm our approach.

Suggested Citation

  • Xue, Yujie & Taniguchi, Masanobu & Liu, Tong, 2024. "Shrinkage estimators of BLUE for time series regression models," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    • Handle: RePEc:eee:jmvana:v:202:y:2024:i:c:s0047259x23001288
    DOI: 10.1016/j.jmva.2023.105282
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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.
    2. 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.
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