Abstract
When a simple Markov or semi-Markov model is fitted to a large set of data over several points in time, confidence intervals based on the asymptotic distribution of the maximum likelihood estimates are generally too narrow. Accordingly, the estimated precision of forecasts is too optimistic. These problems arise not only because of inhomogeneities in the sample, but also because of time inhomogeneities in the parameter values themselves. In this paper, some approaches to finding more realistic interval estimates will be surveyed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
I.V. Basawa and B.L.S.P. Rao,Statistical Inference for Stochastic Processes (Academic Press, New York, 1980).
W.G. Cochran,Sampling Techniques (Wiley, New York, 1977).
A.P. Dempster, N.M. Laird and D.B. Rubin, Maximum likelihood from incomplete data via the EM algorithm (with discussion), J. Roy. Statist. Soc. B 39(1977)1.
R.J. Mislevy, Estimation of latent group effects, J. Amer. Statist. Assoc. 80(1985)993.
P.S.R.S. Rao, J. Kaplan and W.G. Cochran, Estimators for the one-way random effects model with unequal error variances, J. Amer. Statist. Assoc. 76(1981)89.
P.S.R.S. Rao, Theory of the MINQUE — A review, Sankhya, Ser. B (1977) 201.
M.E. Thompson, Estimation of the parameters of a semi-Markov process from censored records, Adv. Appl. Prob. 13(1981)804.
M. West, P.J. Harrison and H.S. Migon, Dynamic generalized linear models and Bayesian forecasting (with discussion), J. Amer. Statist. Assoc. 80(1985)73.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Thompson, M.E. Uncertainty estimation for stochastic process parameters. Ann Oper Res 8, 195–205 (1987). https://doi.org/10.1007/BF02187091
Issue Date:
DOI: https://doi.org/10.1007/BF02187091