Multiple‐shrinkage estimators of means in exponential families
作者:
Fanny Ki And,
Kam‐Wah Tsui,
期刊:
Canadian Journal of Statistics
(WILEY Available online 1990)
卷期:
Volume 18,
issue 1
页码: 31-46
ISSN:0319-5724
年代: 1990
DOI:10.2307/3315415
出版商: Wiley‐Blackwell
关键词: Multiple shrinkage estimator;one‐parameter exponential family;simultaneous estimation;separate shrinkage estimator;combined shrinkage estimator
数据来源: WILEY
摘要:
AbstractShrinkage estimators are often obtained by adjusting the usual estimator towards a target subspace to which the true parameter might belong. However, meaningful reductions in risk below the usual estimator can typically be achieved in a very small part of the parameter space. In the multivariate‐normal mean estimation problem, E. George, in a series of papers, showed how multiple‐shrinkage estimators (data‐weighted averages of several different shrinkage estimators) can attain substantial risk reductions in a large part of the parameter space. This paper extends the multiple‐shrinkage results to the case of simultaneous estimation of the means of several one‐parameter exponential families. Our results are developed by using an identity similar to that of Haff and Johnson (1986). A computer simulation is reported to indicate the magnitude of reductions in risk. Our results are also applied to the problem of how to choose appropriate component variables to combine before a suitable shrinkage estimator is c
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