On the Monge-Amp¨¨re equation for characterizing gamma-Gaussian model

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• 作者：C&eacute ; lestin C. Kokonendji^a ; ^{celestin.kokonendji@univ-fcomte.fr} ; ^{kokonendji@gmail.com} ; Afif Masmoudi^b ; ^{afif.masmoudi@fss.rnu.tn}
• 关键词：primary ; 62H05 ; 60E07 ; secondary ; 62F10 ; 62H99
• 刊名：Statistics and Probability Letters
• 出版年：2013
• 出版时间：July, 2013
• 年：2013
• 卷：83
• 期：7
• 页码：1692-1698
• 全文大小：387 K

文摘

We study the -dimensional gamma-Gaussian model () composed by distributions of random vector , where is a univariate gamma distributed, and given are real independent Gaussian variables with variance . We first solve a particular Monge-Amp¨¨re equation which characterizes this gamma-Gaussian model through the determinant of its covariance matrix, named the generalized variance function. Then, we show that its modified L¨¦vy measure is of the same type for which we prove a conjecture on generalized variance estimators of the gamma-Gaussian model. Finally, we provide reasonable extensions of the model and corresponding problems.