Rao, C. Radhakrishna
(1976)
*Characterization of prior distributions and solution to a compound decision problem*
Annals of Statistics, 4
(5).
pp. 823-835.
ISSN 0090-5364

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Official URL: http://www.jstor.org/pss/2958622

## Abstract

Let y = θ + e where θ and e are independent random variables so that the regression of y on θ is linear and the conditional distribution of y given θ is homoscedastic. We find prior distributions of θ which induce a linear regression of θ on y. If in addition, the conditional distribution of θ given y is homoscedastic (or weakly so), then θ has a normal distribution. The result is generalized to the Gauss-Markoff model Y = Xθ + ε where θ and ε are independent vector random variables. Suppose y_{i} is the average of p observations drawn from the ith normal population with mean θ_{i} and variance σ_{0}^{2} for i = 1,..., k, and the problem is the simultaneous estimation of θ_{1},..., θ_{k}. An estimator alternative to that of James and Stein is obtained and shown to have some advantage.

Item Type: | Article |
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Source: | Copyright of this article belongs to Institute of Mathematical Statistics. |

ID Code: | 58120 |

Deposited On: | 31 Aug 2011 12:31 |

Last Modified: | 31 Aug 2011 12:31 |

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