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Robust multivariate transformations to normality: Constructed variables and likelihood ratio tests

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  • Marco Riani

    (Universitá di Parma)

Abstract

. The assumption of multivariate normality provides the customary powerful and convenient ways of analysing multivariate data: if the data are not normal, the analysis may often be simplified by an appropriate transformation. In this context, the most widely used test is the likelihood ratio, which requires the maximum likelihood estimate of the transformation parameter for each variable. Given that this estimate can only be found numerically, when the number of variables is large (> 20) it is impossible or infeasible to compute the test. In this paper we introduce alternative tests which do not require the maximum likelihood estimate of the transformation parameters and prove algebraically their relationships. We also give insights both using theoretical arguments and a robust simulation study, based on the forward search algorithm, about the distribution of the tests previously introduced.

Suggested Citation

  • Marco Riani, 2004. "Robust multivariate transformations to normality: Constructed variables and likelihood ratio tests," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 13(2), pages 179-196, September.
    • Handle: RePEc:spr:stmapp:v:13:y:2004:i:2:d:10.1007_s10260-004-0095-1
    DOI: 10.1007/s10260-004-0095-1
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    Cited by:

    1. Shun Matsuura & Hiroshi Kurata, 2020. "Covariance matrix estimation in a seemingly unrelated regression model under Stein’s loss," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(1), pages 79-99, March.
    2. Tingguo Zheng & Tao Song, 2014. "A Realized Stochastic Volatility Model With Box-Cox Transformation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(4), pages 593-605, October.

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