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

Masanobu Taniguchi and Junichi Hirukawa

Biometrika, 2005, vol. 92, issue 3, 737-746

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.

Date: 2005
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