Summary
We consider the weighted least squares (WLS) estimation of the transition probabilities of binary processes on the basis of given sample paths in connection with log linear and logistic model analyses. We investigate, in particular, its effectiveness in the analyses supported by a Bayesian method with a smoothness prior over the time domain.
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References
Akaike, H. (1980). Likelihood and Bayes procedure inBayesian Statistics, (eds. J. M. Bernado, M. H. De Groot, D. U. Lindley and A. F. M. Smith), University Press, Valencia, Spain.
Anderson, T. W. and Goodman, L. A. (1957). Statistical inference about Markov chain,Ann. Math. Statist.,28, 89–110.
Basawa, I. V. and Rao, B. L. S. P. (1980).Statistical Inference for Stochastic Processes, Academic Press, London.
Doob, J. L. (1953).Stochastic Processes, John Wiley and Sons, New York.
Imrey, P. B., Koch, G. G. and Stokes, M. E. (1981). Categorical data analysis; some reflections on the log linear model and logistic regression, Part I; Historical and methodological overview,Int. Statist. Rev.,49, 265–283.
Ishiguro, M. and Akaike, H. (1980). Trading day adjustment for the Beyesian seasonal adjustment program BAYSEA,Research Memorandom, No. 189, The Institute of Statistical Mathematics, Tokyo.
Kishino, H. (1982). Statistical analysis of sample paths,Research Memorandom, No. 229, The Institute of Statistical Mathematics, Tokyo.
Lee, T. C., Judge, G. C. and Zellner, A. (1970). Estimating the Parameters of the Markov Probability Model from Aggregate Time Series Data, North Holland, Amsterdam.
Madansky, A. (1959). Least squares estimation in finite Markov processes,Psychometrika,24, 137–144.
Miller, G. A. (1952). Finite Markov processes in psychology,Psychometrika,17, 149–167.
Shiller, R. J. (1973). A distributed lag estimation derived from smoothness priors,Econometrica,41, 775–788.
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Kishino, H. The least squares estimation of the transition probabilities of binary processes on the basis of sample paths. Ann Inst Stat Math 35, 425–438 (1983). https://doi.org/10.1007/BF02480999
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DOI: https://doi.org/10.1007/BF02480999