Consistent and Asymptotically Normal Parameter Estimates for Markov Modulated Poisson Processes

It has recently been shown that the maximum-likelihood estimate (MLE) of the parameters of a Markov modulated Poisson process is consistent, but no results concerning asymptotic normality are known. In this paper we propose a new class of estimates which are consistent, asymptotically normal, and which are almost as good as the MLE.

[1]  Sلأren Asmussen,et al.  Applied Probability and Queues , 1989 .

[2]  Erhan Çinlar,et al.  Introduction to stochastic processes , 1974 .

[3]  Tobias Rydén.  On identifiability and order of continuous-time aggregated Markov chains, Markov-modulated Poisson processes, and phase-type distributions , 1996 .

[4]  T. Rydén.  Parameter Estimation for Markov Modulated Poisson Processes , 1994 .

[5]  E. L. Lehmann,et al.  Theory of point estimation , 1950 .

[6]  G. Lindgren.  Markov regime models for mixed distributions and switching regressions , 1978 .

[7]  Georg Lindgren,et al.  Recursive estimation of parameters in Markov-modulated Poisson processes , 1995, IEEE Trans. Commun..

[8]  N. Ramesh.  Statistical analysis on Markov-modulated Poisson processes , 1995 .

[9]  Calyampudi Radhakrishna Rao,et al.  Linear Statistical Inference and its Applications , 1967 .

[10]  I. Ibragimov,et al.  Independent and stationary sequences of random variables , 1971 .

[11]  A. Wald.  Note on the Consistency of the Maximum Likelihood Estimate , 1949 .

[12]  B. Leroux.  Maximum-likelihood estimation for hidden Markov models , 1992 .

[13]  David M. Lucantoni,et al.  A Markov Modulated Characterization of Packetized Voice and Data Traffic and Related Statistical Multiplexer Performance , 1986, IEEE J. Sel. Areas Commun..

[14]  A. W. Kemp,et al.  Applied Probability and Queues , 1989 .

[15]  Riccardo Gusella,et al.  Characterizing the Variability of Arrival Processes with Indexes of Dispersion , 1991, IEEE J. Sel. Areas Commun..

[16]  K. Meier-Hellstern.  A fitting algorithm for Markov-modulated poisson processes having two arrival rates , 1987 .