Statistical reasoning in dependent p-generalized elliptically contoured distributions and beyond

Wolf-Dieter Richter ()
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Wolf-Dieter Richter: University of Rostock, Institute of Mathematics

Journal of Statistical Distributions and Applications, 2017, vol. 4, issue 1, 1-25

Abstract: Abstract First, likelihood ratio statistics for checking the hypothesis of equal variances of two-dimensional Gaussian vectors are derived both under the standard σ 1 2 , σ 2 2 , ϱ $\left (\sigma ^{2}_{1},\sigma ^{2}_{2},\varrho \right)$ -parametrization and under the geometric (a,b,α)-parametrization where a 2 and b 2 are the variances of the principle components and α is an angle of rotation. Then, the likelihood ratio statistics for checking the hypothesis of equal scaling parameters of principle components of p-power exponentially distributed two-dimensional vectors are considered both under independence and under rotational or correlation type dependence. Moreover, the role semi-inner products play when establishing various likelihood equations is demonstrated. Finally, the dependent p-generalized polar method and the dependent p-generalized rejection-acceptance method for simulating star-shaped distributed vectors are presented.

Keywords: Modeling with correlation and variances of Euclidean coordinates; Modeling with rotation and variances of principle components; Geometric parametrization; Likelihood ratio; p-generalized Fisher distribution; Semi-inner product; Dependent p-generalized polar method; Dependent p-generalized rejection-acceptance simulation; Star-shaped distributions; 02.50.-r; 02.50.Ng; 02.70.-Rr; 02.70.Uv; 62F03; 62F10; 62H15; 62E10 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1186/s40488-017-0074-3

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