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The least squares estimation of the transition probabilities of binary processes on the basis of sample paths

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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

  1. 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.

    MATH  Google Scholar 

  2. Anderson, T. W. and Goodman, L. A. (1957). Statistical inference about Markov chain,Ann. Math. Statist.,28, 89–110.

    Article  MathSciNet  Google Scholar 

  3. Basawa, I. V. and Rao, B. L. S. P. (1980).Statistical Inference for Stochastic Processes, Academic Press, London.

    MATH  Google Scholar 

  4. Doob, J. L. (1953).Stochastic Processes, John Wiley and Sons, New York.

    MATH  Google Scholar 

  5. 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.

    Article  Google Scholar 

  6. 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.

    Google Scholar 

  7. Kishino, H. (1982). Statistical analysis of sample paths,Research Memorandom, No. 229, The Institute of Statistical Mathematics, Tokyo.

    Google Scholar 

  8. 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.

    MATH  Google Scholar 

  9. Madansky, A. (1959). Least squares estimation in finite Markov processes,Psychometrika,24, 137–144.

    Article  MathSciNet  Google Scholar 

  10. Miller, G. A. (1952). Finite Markov processes in psychology,Psychometrika,17, 149–167.

    Article  MathSciNet  Google Scholar 

  11. Shiller, R. J. (1973). A distributed lag estimation derived from smoothness priors,Econometrica,41, 775–788.

    Article  Google Scholar 

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The Institute of Statistical Mathematics

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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

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