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Testing Hypotheses About Structure Of Parameters In Models With Block Compound Symmetric Covariance Structure

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  • Zmyślony Roman

    (Faculty of Mathematics Computer Science and Econometrics, University of Zielona Góra, Szafrana 4a, 65-516, Zielona Góra, Poland .)

  • Kozioł Arkadiusz

    (Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Szafrana 4a, 65-516, Zielona Góra, Poland .)

Abstract

In this article we deal with testing the hypotheses of the so-called structured mean vector and the structure of a covariance matrix. For testing the above mentioned hypotheses Jordan algebra properties are used and tests based on best quadratic unbiased estimators (BQUE) are constructed. For convenience coordinate-free approach (see Kruskal (1968) and Drygas (1970)) is used as a tool for characterization of best unbiased estimators and testing hypotheses. To obtain the test for mean vector, linear function of mean vector with the standard inner product in null hypothesis is changed into equivalent hypothesis about some quadratic function of mean parameters (it is shown that both hypotheses are equivalent and testable). In both tests the idea of the positive and negative part of quadratic estimators is applied to get the test, statistics which have F distribution under the null hypothesis. Finally, power functions of the obtained tests are compared with other known tests like LRT or Roy test. For some set for parameters in the model the presented tests have greater power than the above mentioned tests. In the article we present new results of coordinate-free approach and an overview of existing results for estimation and testing hypotheses about BCS models.

Suggested Citation

  • Zmyślony Roman & Kozioł Arkadiusz, 2019. "Testing Hypotheses About Structure Of Parameters In Models With Block Compound Symmetric Covariance Structure," Statistics in Transition New Series, Polish Statistical Association, vol. 20(2), pages 139-153, June.
    • Handle: RePEc:vrs:stintr:v:20:y:2019:i:2:p:139-153:n:9
    DOI: 10.21307/stattrans-2019-019
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    References listed on IDEAS

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    1. Roy, Anuradha & Leiva, Ricardo & Žežula, Ivan & Klein, Daniel, 2015. "Testing the equality of mean vectors for paired doubly multivariate observations in blocked compound symmetric covariance matrix setup," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 50-60.
    2. Roy, Anuradha & Zmyślony, Roman & Fonseca, Miguel & Leiva, Ricardo, 2016. "Optimal estimation for doubly multivariate data in blocked compound symmetric covariance structure," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 81-90.
    3. Hélène Massam & Erhard Neher, 1997. "On Transformations and Determinants of Wishart Variables on Symmetric Cones," Journal of Theoretical Probability, Springer, vol. 10(4), pages 867-902, October.
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