# 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

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topUchida, 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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