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april 1999 Estimating equations based on eigenfunctions for a discretely observed diffusion process
Mathieu Kessler, Michael Sørensen
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Bernoulli 5(2): 299-314 (april 1999).

Abstract

A new type of martingale estimating function is proposed for inference about classes of diffusion processes based on discrete-time observations. These estimating functions can be tailored to a particular class of diffusion processes by utilizing a martingale property of the eigenfunctions of the generators of the diffusions. Optimal estimating functions in the sense of Godambe and Heyde are found. Inference based on these is invariant under transformations of data. A result on consistency and asymptotic normality of the estimators is given for ergodic diffusions. The theory is illustrated by several examples and by a simulation study.

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Mathieu Kessler. Michael Sørensen. "Estimating equations based on eigenfunctions for a discretely observed diffusion process." Bernoulli 5 (2) 299 - 314, april 1999.

Information

Published: april 1999
First available in Project Euclid: 5 March 2007

zbMATH: 0980.62074
MathSciNet: MR1681700

Keywords: generator , optimal estimating function , quasilikelihood , Stochastic differential equation

Rights: Copyright © 1999 Bernoulli Society for Mathematical Statistics and Probability

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Vol.5 • No. 2 • april 1999
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