The superharmonic condition for simultaneous estimation of means in exponential familles
作者:
L. R. Haff,
R. W. Johnson,
期刊:
Canadian Journal of Statistics
(WILEY Available online 1986)
卷期:
Volume 14,
issue 1
页码: 43-54
ISSN:0319-5724
年代: 1986
DOI:10.2307/3315035
出版商: Wiley‐Blackwell
关键词: Primary 62C15; Secondary 62F10;62C25
数据来源: WILEY
摘要:
AbstractThe mean vector associated with several independent variates from the exponential subclass of Hudson (1978) is estimated under weighted squared error loss. In particular, the formal Bayes and “Stein‐like” estimators of the mean vector are given. Conditions are also given under which these estimators dominate any of the “natural estimators”.Our conditions for dominance are motivated by a result of Stein (1981), who treated the Np(θ,I) case withp≥ 3. Stein showed that formal Bayes estimators dominate the usual estimator if the marginal density of the data is superharmonic. Our present exponential class generalization entails an elliptic differential inequality in some natural variables.Actually, we assume that each component of the data vector has a probability density function which satisfies a certain differential equation. While the densities of Hudson (1978) are particular solutions of this equation, other solutions are not of the exponential class if certain parameters are unknown. Our approach allows for the possibility of extending the parametric Stein‐theory to useful nonexponential cases, but the problem of nuisance parameters is no
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