Abstract
The problem of nonparametric stationary distribution function estimation by the observations of an ergodic diffusion process is considered. The local asymptotic minimax lower bound on the risk of all the estimators is found and it is proved that the empirical distribution function is asymptotically efficient in the sense of this bound.
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Negri, I. Stationary Distribution Function Estimation for Ergodic Diffusion Process. Statistical Inference for Stochastic Processes 1, 61–84 (1998). https://doi.org/10.1023/A:1009997126882
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DOI: https://doi.org/10.1023/A:1009997126882