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On optimality of the empirical distribution function for the estimation of the invariant distribution function of a diffusion process
Abstract
diffusion process. It is also an efficient estimator in the sense that the risk of this estimator attains an asymptotic minimax lower bound. In this paper we review some results on the problem of the efficiency of the empirical distribution function considering three types of risk function. The first one is in a semi-parametric set-up. The second one is the
integrated mean square error and the third is based on the sup norm.
Key words: invariant distribution function, efficiency, lower bound, efficient estimator.