Parameter estimation for Fisher–Snedecor diffusion

Abstract

We consider the problem of parameter estimation for an ergodic diffusion with Fisher–Snedecor invariant distribution, to be called Fisher–Snedecor diffusion. We propose moments-based estimators of unknown parameters, based on both discrete and continuous observations, and prove their consistency and asymptotic normality. The explicit form of the asymptotic covariance matrix is determined by using the properties of eigenfunctions (Fisher–Snedecor polynomials) of the corresponding Sturm–Liouville operator.

Keywords:

• Fisher–Snedecor polynomials
• method of moments
• Pearson's sample correlation coefficient
• transition density

Mathematics Subject Classifications (2010) :

• 60G10
• 60J60
• 62M05
• 62M15

Acknowledgements

This research has been supported by the grant of the European Commission PIRSES-GA-2008-230804 (Marie Curie) and the grant of the Croatian Foundation for Science, Higher Education and Technological Development.