MINIMUM DISTANCE PARAMETER-ESTIMATION FOR DIFFUSION TYPE OBSERVATIONS

We introduce a new class of parameter estimates for diffusion type processes of observations-minimum distance estimates and study the properties of these estimates as the diffusion coefficient tends to zero. Under regularity conditions it is proved that these estimates are consistent, asymptotically normal and local asymptotic minimax in appropriate sense (robust). The asymptotic expansion of these estimates by the powers of diffusion coefficient is obtained.