### Abstract

This paper extensively investigates the theory of estimating the regression coefficient matrix in the normal GMANOVA model. We explicitly construct estimators which improve upon the maximum likelihood estimator under an invariant scalar loss function. These include the double shrinkage estimators and those shrinking the maximum likelihood estimators directly. The underlying method is the decomposition of the problem into the conditional subproblems due to Kariya, Konno, and Strawderman(1996) and application of integration-by-parts technique to derive an unbiased estimate of the risk for certain class of invariant estimators.

Original language | English (US) |
---|---|

Pages (from-to) | 597-611 |

Number of pages | 15 |

Journal | Communications in Statistics - Theory and Methods |

Volume | 28 |

Issue number | 3-4 |

DOIs | |

State | Published - Jan 1 1999 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Statistics and Probability

### Keywords

- Double shrinkage estimators
- GMANOVA model
- Integration-by-parts technique
- Stein effect
- Unbiased estimate of risk

### Cite this

*Communications in Statistics - Theory and Methods*,

*28*(3-4), 597-611. https://doi.org/10.1080/03610929908832316

}

*Communications in Statistics - Theory and Methods*, vol. 28, no. 3-4, pp. 597-611. https://doi.org/10.1080/03610929908832316

**Construction of shrinkage estimators for the regression coefficient matrix in the GMANOVA model.** / Kariya, Takeaki; Konno, Yoshihiko; Strawderman, William.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Construction of shrinkage estimators for the regression coefficient matrix in the GMANOVA model

AU - Kariya, Takeaki

AU - Konno, Yoshihiko

AU - Strawderman, William

PY - 1999/1/1

Y1 - 1999/1/1

N2 - This paper extensively investigates the theory of estimating the regression coefficient matrix in the normal GMANOVA model. We explicitly construct estimators which improve upon the maximum likelihood estimator under an invariant scalar loss function. These include the double shrinkage estimators and those shrinking the maximum likelihood estimators directly. The underlying method is the decomposition of the problem into the conditional subproblems due to Kariya, Konno, and Strawderman(1996) and application of integration-by-parts technique to derive an unbiased estimate of the risk for certain class of invariant estimators.

AB - This paper extensively investigates the theory of estimating the regression coefficient matrix in the normal GMANOVA model. We explicitly construct estimators which improve upon the maximum likelihood estimator under an invariant scalar loss function. These include the double shrinkage estimators and those shrinking the maximum likelihood estimators directly. The underlying method is the decomposition of the problem into the conditional subproblems due to Kariya, Konno, and Strawderman(1996) and application of integration-by-parts technique to derive an unbiased estimate of the risk for certain class of invariant estimators.

KW - Double shrinkage estimators

KW - GMANOVA model

KW - Integration-by-parts technique

KW - Stein effect

KW - Unbiased estimate of risk

UR - http://www.scopus.com/inward/record.url?scp=0041496585&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041496585&partnerID=8YFLogxK

U2 - 10.1080/03610929908832316

DO - 10.1080/03610929908832316

M3 - Article

AN - SCOPUS:0041496585

VL - 28

SP - 597

EP - 611

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

SN - 0361-0926

IS - 3-4

ER -