Efficiency of a Class of Unbiased Estimators for the Invariant Distribution Function of a Diffusion Process

We consider the problem of the estimation of the invariant distribution function of an ergodic diffusion process when the drift coefficient is unknown. The empirical distribution function is a natural estimator which is unbiased, uniformly consistent and efficient in different metrics. Here we study...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2010-01, Vol.39 (1), p.177-185
Main Author: Negri, Ilia
Format: Article
Language:English
Subjects:
Asymptotically efficient estimators
Decision theory
Economic models
Efficiency
Ergodic diffusion
Exact sciences and technology
General topics
Lower bound
Markov processes
Mathematics
Mean square errors
Nonparametric inference
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Statistics
Studies
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Summary:We consider the problem of the estimation of the invariant distribution function of an ergodic diffusion process when the drift coefficient is unknown. The empirical distribution function is a natural estimator which is unbiased, uniformly consistent and efficient in different metrics. Here we study the properties of optimality for another kind of estimator recently proposed. We consider a class of unbiased estimators and we show that they are also efficient in the sense that their asymptotic risk, defined as the integrated mean square error, attains the same asymptotic minimax lower bound of the empirical distribution function.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610920802653852