### 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.

Original language | English |
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Pages (from-to) | 737-746 |

Number of pages | 10 |

Journal | Biometrika |

Volume | 92 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2005 Sep 1 |

### Keywords

- 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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## Cite this

*Biometrika*,

*92*(3), 737-746. https://doi.org/10.1093/biomet/92.3.737