Estimation of variance in bivariate normal distribution after the preliminary test of homogeneity

A preliminary test estimator of variance in the bivariate normal distribution is proposed after the Pitman-Morgan test of homogeneity of two variances. The bias and mean square error of the estimator are derived. The relative efficiency (RE) of the preliminary test estimator is studied. Computations...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2017-02, Vol.46 (3), p.1290-1305
Main Authors: Romero-Padilla, Juan Manuel, Han, Chein-Pai
Format: Article
Language:English
Subjects:
62F03
62F10
62F12
Alliances
Bias and mean square error
Efficiency
Estimators
Homogeneity
Mean square errors
moments of Wishart distribution
Normal distribution
pooling correlated sample variances
preliminary test estimator
relative efficiency
Samples
Statistical methods
Statistics
Variance
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Summary:A preliminary test estimator of variance in the bivariate normal distribution is proposed after the Pitman-Morgan test of homogeneity of two variances. The bias and mean square error of the estimator are derived. The relative efficiency (RE) of the preliminary test estimator is studied. Computations and 3D graphs of RE for different parameters are analyzed. In order to get the maximum RE, recommendations of the significance level for the preliminary test are given for various sample sizes by using the max-min criterion.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2015.1014114