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

Masanobu Taniguchi, Junichi Hirukawa

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    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 Sep



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

    ASJC Scopus subject areas

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

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