The Annals of Statistics

Estimators of diffusions with randomly spaced discrete observations: A general theory

Yacine Aït-Sahalia and Per A. Mykland

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Abstract

We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may possibly be random. We introduce a new operator, the generalized infinitesimal generator, to obtain Taylor expansions of the asymptotic moments of the estimators. As a special case, our results apply to the situation where the data are discretely sampled at a fixed nonrandom time interval. We include as specific examples estimators based on maximum-likelihood and discrete approximations such as the Euler scheme.

Article information

Source
Ann. Statist., Volume 32, Number 5 (2004), 2186-2222.

Dates
First available in Project Euclid: 27 October 2004

Permanent link to this document
https://projecteuclid.org/euclid.aos/1098883787

Digital Object Identifier
doi:10.1214/009053604000000427

Mathematical Reviews number (MathSciNet)
MR2102508

Zentralblatt MATH identifier
1062.62155

Subjects
Primary: 62F12: Asymptotic properties of estimators 62M05
Secondary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60J60

Keywords
Diffusions likelihood discrete and random sampling

Citation

Aït-Sahalia, Yacine; Mykland, Per A. Estimators of diffusions with randomly spaced discrete observations: A general theory. Ann. Statist. 32 (2004), no. 5, 2186--2222. doi:10.1214/009053604000000427. https://projecteuclid.org/euclid.aos/1098883787


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References

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