Expansion of distribution of maximum likelihood estimate for misspecified diffusion type observation
Azzouz Dermoune, Yu. Kutoyanis · Stochastics and stochastics reports · 1995
We consider the problem of parameter estimation by the observations of diffusion type process in the situation when the statistician does not know the true parametric family of observed process. At first we obtain the expansion of the MLE by the powers of the small diffusion coefficient and then using the Malliavin calculus we derive the asymptotic expansion of the distribution function the density and the moments of MLE