On the Monge–Ampère equation for characterizing gamma-Gaussian model

Célestin C. Kokonendji and Afif Masmoudi

Statistics & Probability Letters, 2013, vol. 83, issue 7, 1692-1698

Abstract: We study the k-dimensional gamma-Gaussian model (k>1) composed by distributions of random vector X=(X1,X2,…,Xk)⊤, where X1 is a univariate gamma distributed, and (X2,…,Xk) given X1 are k−1 real independent Gaussian variables with variance X1. We first solve a particular Monge–Ampère 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 Lévy 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.

Keywords: Covariance matrix; Determinant; Generalized variance estimator; Log-Laplace transform; Multivariate natural exponential model (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:83:y:2013:i:7:p:1692-1698

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DOI: 10.1016/j.spl.2013.03.023

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