Efficiency of the empirical distribution for ergodic diffusion
type: Item
instance of: scholarly article
title: Efficiency of the empirical distribution for ergodic diffusion
zbMATH Open document ID: 0910.62079
DOI: 10.2307/3318459
author: Yu. A. Kutoyants
published in: Bernoulli
publication date: 1998-03-04T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bj/1175882218
review text: We consider the problem of estimation of a one-dimensional distribution function \(F(x)\) by the observation of a diffusion process \(\{X_t,0 \leq t\leq T\}\) as \(T\to\infty\). We suppose that the process \(X_t\), \(t\geq 0\), possesses ergodic properties with invariant measure \({\mathbf P}^*\) and \(F(x)= {\mathbf P}^*((-\infty,x])\). We introduce a lower (minimax) bound on the risks of all estimators, then we define the asymptotically efficient estimators as estimators attaining this bound, and finally we show that the empirical distribution function is asymptotically efficient in this problem.
Mathematics Subject Classification ID: 62M05
Mathematics Subject Classification ID: 62G05
zbMATH DE Number: 1123675
zbMATH Keywords: ergodic diffusion process
zbMATH Keywords: minimax bound
zbMATH Keywords: empirical distribution
MaRDI profile type: Publication
OpenAlex ID: W2043827583
description: scientific article; zbMATH DE number 1123675