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The Stein–James estimator for short- and long-memory Gaussian processes

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  • Masanobu Taniguchi
  • Junichi Hirukawa

Abstract

We investigate the mean squared error of the Stein--James estimator for the mean when the observations are generated from a Gaussian vector stationary process with dimension greater than two. First, assuming that the process is short-memory, we evaluate the mean squared error, and compare it with that for the sample mean. Then a sufficient condition for the Stein--James estimator to improve upon the sample mean is given in terms of the spectral density matrix around the origin. We repeat the analysis for Gaussian vector long-memory processes. Numerical examples clearly illuminate the Stein--James phenomenon for dependent samples. The results have the potential to improve the usual trend estimator in time series regression models. Copyright 2005, Oxford University Press.

Suggested Citation

  • 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.
    • Handle: RePEc:oup:biomet:v:92:y:2005:i:3:p:737-746
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    File URL: http://hdl.handle.net/10.1093/biomet/92.3.737
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    Citations

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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).
    3. Yan Liu & Yoshiyuki Tanida & Masanobu Taniguchi, 2021. "Shrinkage estimation for multivariate time series," Statistical Inference for Stochastic Processes, Springer, vol. 24(3), pages 733-751, October.
    4. Li, Ming & Li, Jia-Yue, 2017. "Generalized Cauchy model of sea level fluctuations with long-range dependence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 309-335.
    5. 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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