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Shrinkage estimation for multivariate time series

Author

Listed:
  • Yan Liu

    (Waseda University)

  • Yoshiyuki Tanida

    (Waseda University)

  • Masanobu Taniguchi

    (Waseda University)

Abstract

This paper deals with shrinkage estimators for the mean of p-dimensional Gaussian stationary processes. The shrinkage estimators are expressed by a shrinkage function, including the sample mean and the James–Stein estimator as special cases. We evaluate the mean squared error of such shrinkage estimators from the true mean of a p-dimensional Gaussian vector stationary process with $$p \ge 3$$ p ≥ 3 . A sufficient condition for shrinkage estimators improving the mean squared error upon the sample mean is given in terms of the shrinkage function and the spectral density matrix. In addition, a shrinkage estimator, providing the most significant improvement to the sample mean, is proposed as a theoretical result. The remarkable performance of the proposed shrinkage estimator, compared with the sample mean and the James–Stein estimator, is illustrated by a thorough numerical simulation. A real data analysis also witnesses the applicability of the proposed estimator for multivariate time series.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sistpr:v:24:y:2021:i:3:d:10.1007_s11203-021-09248-2
    DOI: 10.1007/s11203-021-09248-2
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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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