UMVU estimation of the ratio of powers of normal generalized variances under correlation. (English) Zbl 1141.62041
Summary: We consider estimation of the ratio of arbitrary powers of two normal generalized variances based on two correlated random samples. First, a result of the author [Decision theoretic estimation of the ratio of variances in a bivariate normal distribution. Ann. Inst. Stat. Math. 53, No. 3, 436–446 (2001; Zbl 0989.62004)] on UMVU estimation of the ratio of variances in a bivariate normal distribution is extended to the case of the ratio of any powers of the two variances. Motivated by these estimators’ forms we derive the UMVU estimator in the multivariate case. We show that it is proportional to the ratio of the corresponding powers of the two sample generalized variances multiplied by a function of the sample canonical correlations. The mean squared errors of the derived UMVU estimator and the maximum likelihood estimator are compared via simulation for some special cases.
MSC:
| 62H12 | Estimation in multivariate analysis |
| 62H20 | Measures of association (correlation, canonical correlation, etc.) |
| 33C90 | Applications of hypergeometric functions |
| 62F10 | Point estimation |
Keywords:
canonical correlations; generalized variance; hypergeometric function of matrix argument; unbiased estimation; Wishart distribution; zonal polynomials; tablesCitations:
Zbl 0989.62004Software:
MOPSReferences:
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