Far East Journal of Theoretical Statistics
Volume 4, Issue 2, Pages 237 - 255
(December 2000)
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MDI
ESTIMATION OF TWO NORMAL MEANS WITH PRELIMINARY CONJECTURED BOUND AND ORDER INFORMATION
Hea-Jung Kim (Korea)
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Abstract: In estimating restricted means of normal
distributions, it is well known that constrained
maximum likelihood estimator (MLE) is inadmissible for
quadratic loss function. This paper studies the
problem of estimating
means of two independent normal distributions
in which the parameters are to be estimated subject to
the order and boundedness restrictions in accordance
with the preliminary conjectured information. A
minimum discrimination information (MDI) approach is
considered to provide a simple way of specifying the
prior information and to suggest a class of shrinkage
type estimators. We advocate the class of estimators
as an alternative to usual constrained MLE for the
parameters. In particular, we find explicit
improvements to the MLE in terms of mean square error
when the true mean value parameters are located in or
vicinity around the preliminary conjectured
information. |
Keywords and phrases: estimation under bound and order
constraint, minimum discrimination information
procedure, cross entropy, mean square error
efficiency. |
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