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Tytuł artykułu

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

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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].
Twórcy
  • Department of Mathematics, Institute of Mathematics, Agriculture University of Wrocław, Grunwaldzka 53, 50-357 Wrocław, Poland
  • Department of Mathematics, Institute of Mathematics, Agriculture University of Wrocław, Grunwaldzka 53, 50-357 Wrocław, Poland
  • Institute of Mathematics, Technical University, Podgórna 50, 65-246 Zielona Góra, Poland
Bibliografia
  • [1] S. Geisser, Estimation in the uniform covariance case, JASA 59 (1964), 477-483.
  • [2] S. Gnot and A. Michalski, Tests based on admissible estimators in two variance components models, Statistics 25 (1994), 213-223.
  • [3] N.L. Johnson and S. Kotz, Distribution in Statistics: continuous univariate distributions - 2, Houghton Mifflin, New York 1970.
  • [4] J.M. Kinderman and J.F. Monahan, Computer generation of random variables using the ratio of uniform deviates, ACH Trans. Math. Soft. 3 (1977), 257-260.
  • [5] E.L. Lehmann, Testing Statistical Hypotheses, Wiley, New York 1986.
  • [6] A. Michalski and R. Zmyślony, Testing hypotheses for variance components in mixed linear models, Statistics 27 (1996), 297-310.
  • [7] A. Michalski and R. Zmyślony, Testing hypotheses for linear functions of parameters in mixed linear models, Tatra Mountains Math. Publ. 17 (1999), 103-110.
  • [8] J. Seely, Quadratic subspaces and completeness, Ann. Math. Statist. 42 (1971), 710-721.
  • [9] R. Zmyślony, On estimation of parameters in linear models, Zastosowania Matematyki 15 (1976), 271-276.
  • [10] R. Zmyślony, Completeness for a family of normal distributions, Banach Center Publications 6 (1980), 355-357.
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1014
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