Kutoyants, Yu. A. Efficient density estimation for ergodic diffusion processes. (English) Zbl 0953.62085 Stat. Inference Stoch. Process. 1, No. 2, 131-155 (1998). The problem of asymptotically efficient estimation of the density of the invariant measure of a diffusion process is considered. An efficient estimator is defined by the minimax lower bound on the risk of all estimators. The author shows that the local-time and kernel-type estimators are asymptotically efficient for the loss functions with polynomial majorants. The asymptotic behavior of a wide class of unbiased estimators with the same limit variances is also discussed. Reviewer: Yurii Lin’kov (Donetsk) Cited in 24 Documents MSC: 62M05 Markov processes: estimation; hidden Markov models 62G07 Density estimation 62G20 Asymptotic properties of nonparametric inference Keywords:diffusion processes; density estimation; minimax bound PDFBibTeX XMLCite \textit{Yu. A. Kutoyants}, Stat. Inference Stoch. Process. 1, No. 2, 131--155 (1998; Zbl 0953.62085) Full Text: DOI