On parameter orthogonality in symmetric and skew models

Jones, MC; Anaya-Izquierdo, K; (2011) On parameter orthogonality in symmetric and skew models. Journal of statistical planning and inference, 141 (2). pp. 758-770. ISSN 0378-3758 DOI: https://doi.org/10.1016/j.jspi.2010.07.021

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Orthogonal and partly orthogonal reparametrisations are provided for certain wide and important families of univariate continuous distributions. First, the orthogonality of parameters in location-scale symmetric families is extended to symmetric distributions involving a third parameter. This sets the scene for consideration of the four-parameter situation in which skewness is also allowed. It turns out that one specific approach to generating such four-parameter families, that of two-piece distributions with a certain parametrisation restriction, has some attractive features with regard to parameter orthogonality which, to the best of our knowledge, are not shared with other four-parameter distributions. Our work also affords partly orthogonal parametrisations of three-parameter two-piece models. (c) 2010 Elsevier B.V. All rights reserved.

Item Type: Article
Keywords: extended location-scale model, skew-t distribution, two-piece distribution, t-distribution, general-class, distributions, inference, tails
Faculty and Department: Faculty of Epidemiology and Population Health > Dept of Infectious Disease Epidemiology
Research Centre: Centre for Statistical Methodology
Web of Science ID: 284386500016
URI: http://researchonline.lshtm.ac.uk/id/eprint/177


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