96
Views
7
CrossRef citations to date
0
Altmetric
INFERENCE

Large Deviations for Empirical Estimators of the Stationary Distribution of a Semi-Markov Process with Finite State Space

Pages 3077-3089 | Received 08 Aug 2007, Accepted 14 Mar 2008, Published online: 15 Aug 2008

References

  • Andersen , P. K. , Borgan , O. , Gill , R. D. , Keiding , N. ( 1993 ). Statistical Models Based on Counting Processes . New York : Springer .
  • Asmussen , S. ( 2000 ). Ruin Probabilities . Singapore : World Scientific .
  • Baldi , P. , Piccioni , M. ( 1999 ). A representation formula for the large deviation rate function for the empirical law of a continuous time Markov chain . Statist. Probab. Lett. 41 ( 2 ): 107 – 115 .
  • Barbu , V. , Limnios , N. ( 2006a ). Maximum likelihood estimation for hidden semi-Markov models . C. R. Math. Acad. Sci. Paris 342 ( 3 ): 201 – 205 .
  • Barbu , V. , Limnios , N. ( 2006b ). Empirical estimation for discrete-time semi-Markov processes with applications in reliability . J. Nonparametr.Statist 18 ( 7/8 ): 483 – 498 .
  • Dembo , A. , Zeitouni , O. ( 1993 ). Large Deviations Techniques and Applications . Boston : Jones and Bartlett .
  • Gill , R. D. ( 1980 ). Nonparametric estimation based on censored observations of Markov renewal processes . Z. Wahrsch. Verw. Geb. 53 ( 1 ): 97 – 116 .
  • Greenwood , P. E. , Wefelmeyer , W. ( 1996 ). Empirical estimators for semi-Markov processes . Math. Meth. Statist. 5 ( 3 ): 299 – 315 .
  • Janssen , J. , Limnios , N. , eds. ( 1999 ). Semi-Markov Models and Applications . Dordrecht : Kluwer Academic .
  • Janssen , J. , Manca , R. ( 2006 ). Applied Semi-Markov Processes . New York : Springer .
  • Janssen , J. , Manca , R. ( 2007 ). Semi-Markov Risk Models for Finance, Insurance and Reliability . New York : Springer .
  • Kesidis , G. , Walrand , J. ( 1993 ). Relative entropy between Markov transition rate matrices . IEEE Trans. Inform. Theor. 39 ( 3 ): 1056 – 1057 .
  • Lagakos , S. W. , Sommer , C. J. , Zelen , M. ( 1978 ). Semi-Markov models for partially censored data . Biometrika 65 ( 2 ): 311 – 317 .
  • Lancaster , P. , Tismenetsky , M. ( 1985 ). The Theory of Matrices , (2nd ed. with Applications) . London : Academic Press .
  • Limnios , N. ( 2006 ). Estimation of the stationary distribution of semi-Markov processes with Borel state space . Statist. Probab. Lett. 76 ( 14 ): 1536 – 1542 .
  • Limnios , N. , Oprişan , G. ( 2001 ). Semi-Markov Processes and Reliability . Boston : Birkhauser .
  • Limnios , N. , Ouhbi , B. ( 2003 ). Empirical estimator of reliability and related functions for semi-Markov systems . In: Lindqvist , B. , Doksum , K. , eds. Mathematical and Statistical Method in Reliability . World Scientific .
  • Limnios , N. , Ouhbi , B. ( 2006 ). Nonparametric estimation of some important indicators in reliability for semi-Markov processes . Statist. Methodol. 3 ( 4 ): 341 – 350 .
  • Limnios , N. , Ouhbi , B. Sadek , A. ( 2005 ). Empirical estimator of stationary distribution for semi-Markov processes . Commun. Statist. Theor. Meth. 34 ( 4 ): 987 – 995 .
  • Moore , E. H. , Pyke , R. ( 1968 ). Estimation of the transition distributions of a Markov renewal processes . Ann. Inst. Statist. Math. 20 : 411 – 424 .
  • Ouhbi , B. , Limnios , N. ( 1999a ). Non-parametric estimation for semi-Markov processes based on their hazard rate function . Statist. Infer. Stoch. Process. 2 ( 2 ): 151 – 173 .
  • Ouhbi , B. , Limnios , N. ( 1999b ). Nonparametric estimation of failure rate in semi-Markov systems . In: Janssen , J. , Limnios , N. , eds. Semi-Markov Model and Applications . Kluwer Academic .
  • Ouhbi , B. , Limnios , N. ( 2002 ). The rate of occurrence of failures for semi-Markov processes and estimation . Statist. Probab. Lett. 59 ( 3 ): 245 – 255 .
  • Ouhbi , B. , Limnios , N. ( 2003 ). Non-parametric reliability estimation of semi-Markov processes . J. Statist. Plann. Inf. 109 ( 1/2 ): 155 – 165 .
  • Sadek , A. , Limnios , N. ( 2005 ). Nonparametric estimation of reliability and survival function for continuous-time finite Markov processes . J. Statist. Plann. Inf. 133 ( 1 ): 1 – 21 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.