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

Masanobu Taniguchi*, Junichi Hirukawa

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)737-746
Number of pages10
Issue number3
Publication statusPublished - 2005 Sept


  • Long-memory process
  • Mean squared error
  • Short-memory process
  • Spectral density matrix
  • Stein-james estimator

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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