Afrika Statistika

On optimality of the empirical distribution function for the estimation of the invariant distribution function of a diffusion process

Ilia Negri

Full-text: Open access

Abstract

In this work we present some results on the optimality of the empirical distribution function as an estimator of the invariant distribution function of an ergodic diffusion process. The results presented were obtained in different previous works under conditions that are rewritten in a unified form that make those results comparable. It is well known that the empirical distribution function 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 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.

Article information

Source
Afr. Stat., Volume 3, Number 1 (2008), 83-104.

Dates
Received: 11 October 2008
Revised: 4 November 2008
First available in Project Euclid: 26 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.as/1495818315

Digital Object Identifier
doi:10.4314/afst.v3i1.46876

Mathematical Reviews number (MathSciNet)
MR2531123

Zentralblatt MATH identifier
1241.62117

Subjects
Primary: 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx]
Secondary: 62M20: Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11]

Keywords
invariant distribution function efficiency lower bound efficient estimator

Citation

Negri, Ilia. On optimality of the empirical distribution function for the estimation of the invariant distribution function of a diffusion process. Afr. Stat. 3 (2008), no. 1, 83--104. doi:10.4314/afst.v3i1.46876. https://projecteuclid.org/euclid.as/1495818315


Export citation