Discussiones Mathematicae Probability and Statistics 20(2) (2000) 233247
Edward Gąsiorek, Andrzej Michalski
Department of Mathematics, Institute of Mathematics
Agriculture University of Wrocław
Grunwaldzka 53, 50357 Wrocław, Poland
email:max@ozi.ar.wroc.pl
and
Roman Zmyślony
Institute of Mathematics, Technical University
Podgórna 50, 65246 Zielona Góra, Poland
email:r.zmyslony@im.uz.zgora.pl
In the paper, a new approach to construction test for independenceof twodimensional normally distributed random vectors is given under the assumption that the ratio of the variances is known. This test is uniformly better than the tStudent test. A comparison of the power of these two tests is given. A behaviour of this test forsome εcontamination of the original model is also shown. In the general case when the variance ratio is unknown, an adaptive test is presented. The equivalence between this test and the classical ttest for independence of normal variables is shown. Moreover, the confidence interval for correlation coefficient is given. The results follow from the unified theory of testing hypotheses both for fixed effects and variance components presented in papers [6] and [7].
Keywords and phrases: mixed linear models; variance components;correlation; quadratic unbiased estimation; testing hypotheses; confidence intervals.
1999 Mathematics Subject Classiffication: 62F03, 62J10.
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Received 5 September 2000