Statistical inference for inverse gamma diffusion process
Nikolai N. Leonenko, Nenad Šuvak · 2008
Stationary diffusion process with invariant marginal inverse gamma distribution is considered. The transition probability is represented as principal solution of corresponding Fokker-Planck equation. Its spectral decomposition in terms of eigenfunctions related to discrete part of the spectrum (i.e. Bessel polynomials) and eigenfunctions related to continuous part of the spectrum is represented. Statistical part includes method of moment estimation of unknown parameters of inverse gamma diffusion. Their consistency and asymptotic normality under mixing properties of corresponding process are analyzed. As conclusion, procedure based on Stein equation for testing inverse gamma distributional assumptions is presented.