### Abstract

The least squares (LS) estimator seems the natural estimator of the coefficients of a Gaussian linear regression model. However, if the dimension of the vector of coefficients is greater than 2 and the residuals are independent and identically distributed, this conventional estimator is not admissible. James and Stein [Estimation with quadratic loss, Proceedings of the Fourth Berkely Symposium vol. 1, 1961, pp. 361-379] proposed a shrinkage estimator (James-Stein estimator) which improves the least squares estimator with respect to the mean squares error loss function. In this paper, we investigate the mean squares error of the James-Stein (JS) estimator for the regression coefficients when the residuals are generated from a Gaussian stationary process. Then, sufficient conditions for the JS to improve the LS are given. It is important to know the influence of the dependence on the JS. Also numerical studies illuminate some interesting features of the improvement. The results have potential applications to economics, engineering, and natural sciences.

Original language | English |
---|---|

Pages (from-to) | 1984-1996 |

Number of pages | 13 |

Journal | Journal of Multivariate Analysis |

Volume | 97 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2006 Oct |

### Fingerprint

### Keywords

- Gaussian stationary process
- James-Stein estimator
- Least squares estimator
- Mean squares error
- Regression spectrum
- Residual spectral density matrix
- Time series regression model

### ASJC Scopus subject areas

- Statistics, Probability and Uncertainty
- Numerical Analysis
- Statistics and Probability

### Cite this

*Journal of Multivariate Analysis*,

*97*(9), 1984-1996. https://doi.org/10.1016/j.jmva.2005.08.011

**James-Stein estimators for time series regression models.** / Senda, Motohiro; Taniguchi, Masanobu.

Research output: Contribution to journal › Article

*Journal of Multivariate Analysis*, vol. 97, no. 9, pp. 1984-1996. https://doi.org/10.1016/j.jmva.2005.08.011

}

TY - JOUR

T1 - James-Stein estimators for time series regression models

AU - Senda, Motohiro

AU - Taniguchi, Masanobu

PY - 2006/10

Y1 - 2006/10

N2 - The least squares (LS) estimator seems the natural estimator of the coefficients of a Gaussian linear regression model. However, if the dimension of the vector of coefficients is greater than 2 and the residuals are independent and identically distributed, this conventional estimator is not admissible. James and Stein [Estimation with quadratic loss, Proceedings of the Fourth Berkely Symposium vol. 1, 1961, pp. 361-379] proposed a shrinkage estimator (James-Stein estimator) which improves the least squares estimator with respect to the mean squares error loss function. In this paper, we investigate the mean squares error of the James-Stein (JS) estimator for the regression coefficients when the residuals are generated from a Gaussian stationary process. Then, sufficient conditions for the JS to improve the LS are given. It is important to know the influence of the dependence on the JS. Also numerical studies illuminate some interesting features of the improvement. The results have potential applications to economics, engineering, and natural sciences.

AB - The least squares (LS) estimator seems the natural estimator of the coefficients of a Gaussian linear regression model. However, if the dimension of the vector of coefficients is greater than 2 and the residuals are independent and identically distributed, this conventional estimator is not admissible. James and Stein [Estimation with quadratic loss, Proceedings of the Fourth Berkely Symposium vol. 1, 1961, pp. 361-379] proposed a shrinkage estimator (James-Stein estimator) which improves the least squares estimator with respect to the mean squares error loss function. In this paper, we investigate the mean squares error of the James-Stein (JS) estimator for the regression coefficients when the residuals are generated from a Gaussian stationary process. Then, sufficient conditions for the JS to improve the LS are given. It is important to know the influence of the dependence on the JS. Also numerical studies illuminate some interesting features of the improvement. The results have potential applications to economics, engineering, and natural sciences.

KW - Gaussian stationary process

KW - James-Stein estimator

KW - Least squares estimator

KW - Mean squares error

KW - Regression spectrum

KW - Residual spectral density matrix

KW - Time series regression model

UR - http://www.scopus.com/inward/record.url?scp=33748432535&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33748432535&partnerID=8YFLogxK

U2 - 10.1016/j.jmva.2005.08.011

DO - 10.1016/j.jmva.2005.08.011

M3 - Article

AN - SCOPUS:33748432535

VL - 97

SP - 1984

EP - 1996

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

SN - 0047-259X

IS - 9

ER -