Estimation for misspecified ergodic diffusion processes from discrete observations

Masayuki Uchida; Nakahiro Yoshida

ESAIM: Probability and Statistics (2012)

  • Volume: 15, page 270-290
  • ISSN: 1292-8100

Abstract

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The joint estimation of both drift and diffusion coefficient parameters is treated under the situation where the data are discretely observed from an ergodic diffusion process and where the statistical model may or may not include the true diffusion process. We consider the minimum contrast estimator, which is equivalent to the maximum likelihood type estimator, obtained from the contrast function based on a locally Gaussian approximation of the transition density. The asymptotic normality of the minimum contrast estimator is proved. In particular, the rate of convergence for the minimum contrast estimator of diffusion coefficient parameter in a misspecified model is different from the one in the correctly specified parametric model.

How to cite

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Uchida, Masayuki, and Yoshida, Nakahiro. "Estimation for misspecified ergodic diffusion processes from discrete observations." ESAIM: Probability and Statistics 15 (2012): 270-290. <http://eudml.org/doc/222478>.

@article{Uchida2012,
abstract = { The joint estimation of both drift and diffusion coefficient parameters is treated under the situation where the data are discretely observed from an ergodic diffusion process and where the statistical model may or may not include the true diffusion process. We consider the minimum contrast estimator, which is equivalent to the maximum likelihood type estimator, obtained from the contrast function based on a locally Gaussian approximation of the transition density. The asymptotic normality of the minimum contrast estimator is proved. In particular, the rate of convergence for the minimum contrast estimator of diffusion coefficient parameter in a misspecified model is different from the one in the correctly specified parametric model. },
author = {Uchida, Masayuki, Yoshida, Nakahiro},
journal = {ESAIM: Probability and Statistics},
keywords = {Diffusion process; misspecified model; discrete time observations; minimum contrast estimator; rate of convergence; diffusion process; rate of convergence},
language = {eng},
month = {1},
pages = {270-290},
publisher = {EDP Sciences},
title = {Estimation for misspecified ergodic diffusion processes from discrete observations},
url = {http://eudml.org/doc/222478},
volume = {15},
year = {2012},
}

TY - JOUR
AU - Uchida, Masayuki
AU - Yoshida, Nakahiro
TI - Estimation for misspecified ergodic diffusion processes from discrete observations
JO - ESAIM: Probability and Statistics
DA - 2012/1//
PB - EDP Sciences
VL - 15
SP - 270
EP - 290
AB - The joint estimation of both drift and diffusion coefficient parameters is treated under the situation where the data are discretely observed from an ergodic diffusion process and where the statistical model may or may not include the true diffusion process. We consider the minimum contrast estimator, which is equivalent to the maximum likelihood type estimator, obtained from the contrast function based on a locally Gaussian approximation of the transition density. The asymptotic normality of the minimum contrast estimator is proved. In particular, the rate of convergence for the minimum contrast estimator of diffusion coefficient parameter in a misspecified model is different from the one in the correctly specified parametric model.
LA - eng
KW - Diffusion process; misspecified model; discrete time observations; minimum contrast estimator; rate of convergence; diffusion process; rate of convergence
UR - http://eudml.org/doc/222478
ER -

References

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