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ArticleOriginal scientific text

Title

Tests of independence of normal random variables with known and unknown variance ratio

Authors 1, 1, 2

Affiliations

  1. Department of Mathematics, Institute of Mathematics, Agriculture University of Wrocław, Grunwaldzka 53, 50-357 Wrocław, Poland
  2. Institute of Mathematics, Technical University, Podgórna 50, 65-246 Zielona Góra, Poland

Abstract

In the paper, a new approach to construction test for independenceof two-dimensional normally distributed random vectors is given under the assumption that the ratio of the variances is known. This test is uniformly better than the t-Student test. A comparison of the power of these two tests is given. A behaviour of this test forsome ε-contamination 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 t-test 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

ENG
mixed linear models, variance components, correlation, quadratic unbiased estimation, testing hypotheses, confidence intervals

Bibliography

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Discussiones Mathematicae Probability and Statistics
2000/20/2
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Pages:
233-247
Main language of publication
English
Received
2000-09-05
Published
2000

DOI: 10.7151/dmps.1014

Exact and natural sciences