Shrinkage estimation for multivariate time series

Yan Liu (), Yoshiyuki Tanida and Masanobu Taniguchi
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Yan Liu: Waseda University
Yoshiyuki Tanida: Waseda University
Masanobu Taniguchi: Waseda University

Statistical Inference for Stochastic Processes, 2021, vol. 24, issue 3, No 8, 733-751

Abstract: 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.

Keywords: Shrinkage estimation; Multivariate stationary processes; Shrinkage function; Sample mean; James–Stein estimator; Spectral density matrix (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11203-021-09248-2

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