Bernoulli

  • Bernoulli
  • Volume 5, Number 2 (1999), 299-314.

Estimating equations based on eigenfunctions for a discretely observed diffusion process

Mathieu Kessler and Michael Sørensen

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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.

Article information

Source
Bernoulli, Volume 5, Number 2 (1999), 299-314.

Dates
First available in Project Euclid: 5 March 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1173147908

Mathematical Reviews number (MathSciNet)
MR1681700

Zentralblatt MATH identifier
0980.62074

Keywords
generator optimal estimating function quasilikelihood stochastic differential equation

Citation

Kessler, Mathieu; Sørensen, Michael. Estimating equations based on eigenfunctions for a discretely observed diffusion process. Bernoulli 5 (1999), no. 2, 299--314. https://projecteuclid.org/euclid.bj/1173147908


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