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

Authors: Taniguchi, Masanobu; Hirukawa, Junichi

Source: Biometrika, Volume 92, Number 3, 1 September 2005 , pp. 737-746(10)

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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.

Keywords: Long-memory process; Mean squared error; Short-memory process; Spectral density matrix; Stein–James estimator

Document Type: Research article

DOI: http://dx.doi.org/10.1093/biomet/92.3.737

Publication date: 2005-09-01