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On spectral properties and statistical analysis of Fisher-Snedecor diffusion

On spectral properties and statistical analysis of Fisher-Snedecor diffusion,F. Avram,N. N. Leonenko,N. Suvak

On spectral properties and statistical analysis of Fisher-Snedecor diffusion   (Citations: 1)
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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.
Published in 2010.
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    • ...The KP family contains specific diffusions that have recently been studied, such as those of Student and Fisher‐ Snedecor (see Avram et al. 2010 for a detailed study of the KP family)...
    • ...fulfilled, to obtain the existence and uniqueness of a strong solution (see Avram et al. 2010, p. 6). Consequently, there exists a separable, measurable and almost surely (a.s.) sample continuous diffusion process fxðtÞ; t 2½ t0; T�g which is the unique (a.s.) strong solution to Ito’s SDE Eq. 8 with infinitesimal moments (drift parameter and diffusion coefficient) given, respectively, by A1ðt; x Þ¼ hðt ...

    R. Gutiérrezet al. Detection, modelling and estimation of non-linear trends by using a no...

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