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
Access Full Article
top
Abstract
topHow to cite
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
top- B.M. Bibby and M. Sørensen, Martingale estimating functions for discretely observed diffusion processes. Bernoulli 1 (1995) 17–39.
- D. Florens-Zmirou, Approximate discrete time schemes for statistics of diffusion processes. Statistics20 (1989) 547–557.
- V. Genon-Catalot and J. Jacod, On the estimation of the diffusion coefficient for multidimensional diffusion processes. Ann. Inst. Henri Poincaré Probab. Statist.29 (1993) 119–151.
- E. Gobet, LAN property for ergodic diffusions with discrete observations. Ann. Inst. H. Poincaré Probab. Statist.38 (2002) 711–737.
- P. Hall and C. Heyde, Martingale limit theory and its applications. Academic Press, New York (1980).
- I.A. Ibragimov and R.Z. Has'minskii, Statistical estimation. Springer Verlag, New York (1981).
- M. Kessler, Estimation of an ergodic diffusion from discrete observations. Scand. J. Statist.24 (1997) 211–229.
- S. Kusuoka and N. Yoshida, Malliavin calculus, geometric mixing, and expansion of diffusion functionals, Probab. Theory Relat. Fields116 (2000) 457–484.
- Yu.A. Kutoyants, Statistical inference for ergodic diffusion processes. Springer-Verlag, London (2004).
- H. Masuda, Ergodicity and exponential β-mixing bound for multidimensional diffusions with jumps. Stochastic Processes Appl. 117 (2007) 35–56.
- I.W. McKeague, Estimation for diffusion processes under misspecified models. J. Appl. Probab. 21 (1984) 511–520.
- S.P. Meyn and P.L. Tweedie, Stability of Markovian processes. III. Foster-Lyapunov criteria for continuous-time processes. Adv. in Appl. Probab.25 (1993) 518–548.
- E. Pardoux and A.Y. Veretennikov, On the Poisson equation and diffusion approximation 1. Ann. Prob. 29 (2001) 1061–1085.
- B.L.S. Prakasa Rao, Asymptotic theory for nonlinear least squares estimator for diffusion processes. Math. Operationsforsch. Statist. Ser. Statist.14 (1983) 195–209.
- B.L.S. Prakasa Rao, Statistical inference from sampled data for stochastic processes. Contemp. Math.80 (1988) 249–284. Amer. Math. Soc., Providence, RI.
- M. Uchida and N. Yoshida, Information criteria in model selection for mixing processes. Statist. Infer. Stochast. Process.4 (2001) 73–98.
- N. Yoshida, Asymptotic behavior of M-estimator and related random field for diffusion process. Ann. Inst. Statist. Math.42 (1990) 221–251.
- N. Yoshida, Estimation for diffusion processes from discrete observation. J. Multivariate Anal.41 (1992) 220–242.
- N. Yoshida, Polynomial type large deviation inequalities and quasi-likelihood analysis for stochastic differential equations (to appear in Ann. Inst. Statist. Math.) (2005).
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.