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Estimation for diffusion processes under misspecified models

Published online by Cambridge University Press:  14 July 2016

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.

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.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1984 

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References

Banon, G. (1978) Nonparametric identification for diffusion processes. SIAM J. Control and Optimization 16, 380395.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, 228238.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, 221233.Google Scholar
Kutoyants, Yu. A. (1977) Estimation of the drift coefficient parameter of a diffusion process in the smooth case. Theory Prob. Appl. 22, 399406.Google Scholar
Lanska, V. (1979) Minimum contrast estimation in diffusion processes. J. Appl. Prob. 16, 6575.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, 170189.Google Scholar
White, H. (1981) Consequences and detection of misspecified nonlinear regression models. J. Amer. Statist. Assoc. 76, 419433.CrossRefGoogle Scholar