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Estimation for Discrete-time Semi-Markov Reward Processes: Analysis and Inference

Author

Listed:
  • K. Khorshidian

    (Shiraz University)

  • F. Negahdari

    (Shiraz University)

  • H. A. Mardnifard

    (Yasouj University)

Abstract

In this paper, the moments of a class of reward processes defined on a discrete-time semi-Markov process and the asymptotic behaviors of the corresponding empirical estimators have been investigated. Some known results concerning the asymptotic distribution and properties of semi-Markov kernel have been obtained by a different approach. By using the empirical estimator of the semi-Markov kernel and the mentioned approach, the estimators for the moments of the reward process have been introduced and their asymptotic properties have been established. As a consequence of the strong consistency and asymptotic normality, the confidence intervals have also been obtained. A numerical example illustrates the results.

Suggested Citation

  • K. Khorshidian & F. Negahdari & H. A. Mardnifard, 2016. "Estimation for Discrete-time Semi-Markov Reward Processes: Analysis and Inference," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 885-900, September.
    • Handle: RePEc:spr:metcap:v:18:y:2016:i:3:d:10.1007_s11009-015-9468-1
    DOI: 10.1007/s11009-015-9468-1
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    References listed on IDEAS

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    1. Brahim Ouhbi & Nikolaos Limnios, 1999. "Nonparametric Estimation for Semi-Markov Processes Based on its Hazard Rate Functions," Statistical Inference for Stochastic Processes, Springer, vol. 2(2), pages 151-173, May.
    2. Guglielmo D'Amico & Jacques Janssen & Raimondo Manca, 2011. "A Non-Homogeneous Semi-Markov Reward Model For The Credit Spread Computation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(02), pages 221-238.
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