Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-29T13:40:19.653Z Has data issue: false hasContentIssue false
  • English
  • Français

Estimation for diffusion processes under misspecified models

Published online by Cambridge University Press:  14 July 2016

Ian W. McKeague
Ian W. McKeague*
Affiliation:
The Florida State University
*
∗Postal address: Department of Statistics and Statistical Consulting Center, The Florida State University, Tallahassee, FL 32306, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

The asymptotic behavior of the maximum likelihood estimator of a parameter in the drift term of a stationary ergodic diffusion process is studied under conditions in which the true drift function and true noise function do not coincide with those specified by the parametric model.

Keywords

STOCHASTIC DIFFERENTIAL EQUATIONSMAXIMUM LIKELIHOOD ESTIMATIONROBUSTNESSASYMPTOTIC NORMALITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 3 , September 1984 , pp. 511 - 520
Copyright
Copyright © Applied Probability Trust 1984 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Banon, G. (1978) Nonparametric identification for diffusion processes. SIAM J. Control and Optimization 16, 380–395.CrossRefGoogle Scholar
Berger, R. L. and Langberg, N. A. (1981) Linear least squares estimates and nonlinear means. Florida State University Statistics Report M-573.Google Scholar
Brown, B. M. and Hewitt, J. I. (1975) Asymptotic likelihood theory for diffusion processes. J. Appl. Prob. 12, 228–238.CrossRefGoogle Scholar
Geman, S. (1980) An application of the method of sieves: functional estimator for the drift of a diffusion. Colloq. Math. Soc. János Bolyai 32. Nonparametric Statistical Inference, Budapest, Hungary.Google Scholar
Huber, P. J. (1967) The behavior of maximum likelihood estimates under nonstandard conditions. Proc. 5th Berkeley Symp. Math. Statist. Prob. 1, 221–233.Google Scholar
Kutoyants, Yu. A. (1977) Estimation of the drift coefficient parameter of a diffusion process in the smooth case. Theory Prob. Appl. 22, 399–406.Google Scholar
Lanska, V. (1979) Minimum contrast estimation in diffusion processes. J. Appl. Prob. 16, 65–75.CrossRefGoogle Scholar
Liptser, R. S. and Shiryayev, A. N. (1977) Statistics of Random Processes I. Springer-Verlag, New York.Google Scholar
Mandl, P. (1968) Analytical Treatment of One-Dimensional Markov Processes. Academia, Prague; Springer-Verlag, Berlin.Google Scholar
Prakasa Rao, B. L. S. and Rubin, H. (1981) Asymptotic theory of estimation in non-linear stochastic differential equations. Sankhya A 43, 170–189.Google Scholar
White, H. (1981) Consequences and detection of misspecified nonlinear regression models. J. Amer. Statist. Assoc. 76, 419–433.CrossRefGoogle Scholar