In this work we present some results on the optimality of the empirical distribution function as estimator of the invariant distribution function of an ergodic diffusion process. The result presented here were obtained in different previous works under conditions that we have uniformed in this work. It is well known that the empirical distribution function it is an unbiased and uniformly consistent estimator for the invariant distribution function of an ergodic diffusion process. It is also an efficient estimator in the sense that the risk of this estimator attain an asymptotic minimax lower bound. In this paper we review some results on the problem of the efficiency of the empirical distribution considering three type of risk functions. 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.
On optimality of the empirical distribution function for the estimation of the invariant distribution function of a diffusion process
NEGRI, Ilia
2008-01-01
Abstract
In this work we present some results on the optimality of the empirical distribution function as estimator of the invariant distribution function of an ergodic diffusion process. The result presented here were obtained in different previous works under conditions that we have uniformed in this work. It is well known that the empirical distribution function it is an unbiased and uniformly consistent estimator for the invariant distribution function of an ergodic diffusion process. It is also an efficient estimator in the sense that the risk of this estimator attain an asymptotic minimax lower bound. In this paper we review some results on the problem of the efficiency of the empirical distribution considering three type of risk functions. 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.File | Dimensione del file | Formato | |
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