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September 1995 Consistency and asymptotic normality of an approximate maximum likelihood estimator for discretely observed diffusion processes
Asger Roer Pedersen
Bernoulli 1(3): 257-279 (September 1995). DOI: 10.3150/bj/1193667818

Abstract

Most often the likelihood function based on discrete observations of a diffusion process is unknown, and estimators alternative to the well-behaved maximum likelihood estimator must be found. Traditionally, such estimators are defined with origin in the theory for continuous observation of the diffusion process, and are as a consequence strongly biased unless the discrete observation time-points are close. In contrast to these estimators, an estimator based on an approximation to the (unknown) likelihood function was proposed in Pedersen (1994). We prove consistency and asymptotic normality of this estimator with no assumptions on the distance between the discrete observation time-points.

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Asger Roer Pedersen. "Consistency and asymptotic normality of an approximate maximum likelihood estimator for discretely observed diffusion processes." Bernoulli 1 (3) 257 - 279, September 1995. https://doi.org/10.3150/bj/1193667818

Information

Published: September 1995
First available in Project Euclid: 29 October 2007

zbMATH: 0839.62079
MathSciNet: MR1363541
Digital Object Identifier: 10.3150/bj/1193667818

Keywords: approximate inference , approximate likelihood , approximate transition density , Discrete observations , Euler-Maruyama , Ornstein-Uhlenbeck , Stochastic differential equation

Rights: Copyright © 1995 Bernoulli Society for Mathematical Statistics and Probability

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Vol.1 • No. 3 • September 1995
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