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Maximum spacing estimation for continuous time Markov chains and semi-Markov processes

Author

Listed:
  • Kristi Kuljus

    (University of Tartu)

  • Bo Ranneby

    (Swedish University of Agricultural Sciences)

Abstract

In this article, the maximum spacing (MSP) method is extended to continuous time Markov chains and semi-Markov processes and consistency of the MSP estimator is proved. For independent and identically distributed univariate observations the idea behind the MSP method is to approximate the Kullback–Leibler information so that each contribution is bounded from above. Following the same idea, the MSP function in this article is defined as an approximation of the relative entropy rate for semi-Markov processes and continuous time Markov chains. The MSP estimator is defined as the parameter value that maximizes the MSP function. Consistency of the MSP estimator is also studied when the assigned model is incorrect.

Suggested Citation

  • Kristi Kuljus & Bo Ranneby, 2021. "Maximum spacing estimation for continuous time Markov chains and semi-Markov processes," Statistical Inference for Stochastic Processes, Springer, vol. 24(2), pages 421-443, July.
    • Handle: RePEc:spr:sistpr:v:24:y:2021:i:2:d:10.1007_s11203-021-09238-4
    DOI: 10.1007/s11203-021-09238-4
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    References listed on IDEAS

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    1. M. Ekström & S. M. Mirakhmedov & S. Rao Jammalamadaka, 2020. "A class of asymptotically efficient estimators based on sample spacings," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 617-636, September.
    2. Kristi Kuljus & Bo Ranneby, 2015. "Generalized Maximum Spacing Estimation for Multivariate Observations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 1092-1108, December.
    3. Kristi Kuljus & Bo Ranneby, 2020. "Asymptotic normality of generalized maximum spacing estimators for multivariate observations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 968-989, September.
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