Estimation of the variance and its applications

For the variance of a normal distribution with an unknown mean, three types of truncated estimators superior to the best affine equivariant are treated and their efficiencies are compared asymptotically and numerically. As an application, the simultaneous estimation of a multivariate normal mean is...

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Bibliographic Details
Published inJournal of statistical planning and inference Vol. 35; no. 3; pp. 319 - 333
Main Authors Kubokawa, T., Morita, K., Makita, S., Nagakura, K.
Format Journal Article
LanguageEnglish
Published Lausanne Elsevier B.V 01.06.1993
New York,NY Elsevier Science
Amsterdam
Subjects
Exact sciences and technology
James-Stein estimator efficiency comparison
Mathematics
multivariate normal mean
Parametric inference
Point estimation
Probability and statistics
Sciences and techniques of general use
shrinkage
Statistics
variance
multivariate normal mean
secondary 62J07
James-Stein estimator efficiency comparison
variance
Point estimation
Primary 62F10
shrinkage
Parameter estimation
Estimator efficiency
Gaussian distribution
Multivariate distribution
Estimateur à rétrécisseur
Statistical simulation
Variance
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Summary:For the variance of a normal distribution with an unknown mean, three types of truncated estimators superior to the best affine equivariant are treated and their efficiencies are compared asymptotically and numerically. As an application, the simultaneous estimation of a multivariate normal mean is considered and it is demonstrated that using an improved estimator of the variance leads to the improvement on the James-Stein estimator for the mean vector. Also simulation results for the relative risk improvement are given.
ISSN:0378-3758
1873-1171
DOI:10.1016/0378-3758(93)90020-7