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arXiv · 1007.4909

On spectral properties and statistical analysis of Fisher-Snedecor diffusion

F. Avram·N. N. Leonenko·N. Šuvak
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Abstract

We consider the problem of parameter estimation for an ergodic diffusion with Fisher-Snedecor invariant distribution, to be called Fisher-Snedecor diffusion. We compute the spectral representation of its transition density, which involves a finite number of discrete eigenfunctions (Fisher-Snedecor polynomials) as well as a continuous part. We propose moments based estimators (related to the Fisher-Snedecor polynomials) and prove their consistency and asymptotic normality. Furthermore, we propose a statistical test for the distributional assumptions on the marginal distribution of the Fisher-Snedecor diffusion, based on the moment condition derived from the corresponding Stein's equation.

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F. Avram, N. N. Leonenko, N. Šuvak. 2010-07-28. On spectral properties and statistical analysis of Fisher-Snedecor diffusion. https://arxiv.org/abs/1007.4909

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