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Moderate deviation for maximum likelihood estimators from single server queues

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  • Consider a single server queueing model which is observed over a continuous time interval (0,T], where T is determined by a suitable stopping rule. Let θ be the unknown parameter for the arrival process and $\hat {\theta }_{T}$ be the maximum likelihood estimator of θ. The main goal of this paper is to obtain a moderate deviation result of the maximum likelihood estimator for the single server queueing model under certain regular conditions.
    Mathematics Subject Classification: 60K25;62F12.


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  • [1]

    Acharya, S.K. (1999). On normal approximation for Maximum likelihood estimation from single server queues, Queueing Syst. 31, 207–216.


    Acharya, S.K. and S.K. Singh. (2019). Asymptotic properties of maximum likelihood estimators from single server queues: A martingale approach, Commun. Stat. Theory Methods 48, 3549–3557.


    Basawa, I.V. and N.U. Prabhu. (1981). Estimation in single server queues, Naval. Res. Logist. Quart. 28, 475–487.


    Basawa, I.V. and N.U. Prabhu. (1988). Large sample inference from single server queues, Queueing Syst. 3, 289–304.


    Billingsley, P. (1961). Statistical Inference for Markov Processes, The University of Chicago Press, Chicago.


    Clarke, A.B. (1957). Maximum likelihood estimates in a simple queue, Ann. Math. Statist 28, 1036–1040.


    Cox, D.R. (1965). Some problems of statistical analysis connected with congestion (W.L. Smith and W. B. Wilkinson, eds.), University of North Carolina Press, Chapel Hill.


    Dembo, A. and O. Zeitouni. (1998). Large deviation Techniques and Applications, 2nd edn, Springer, New York.


    Ellis, R.S. (1984). Large deviations for a general class of random vectors, Ann. Probab. 12, 1–12.


    Gärtner, J. (1977). On large deviations from the invariant measure, Theory Probab. Appl. 22, 24–39.


    Gao, F. (2001). Moderate deviations for the maximum likelihood estimator, Stat. Probab. Lett. 55, 345– 352.


    Goyal, T.L. and C.M. Harris. (1972). Maximum likelihood estimation for queues with state dependent service, Sankhya Ser. A 34, 65–80.


    Hall, P. and C.C. Heyde. (1980). Martingale Limit Theory and Applications, Academic Press, New York.


    Miao, Y. and Y.-X. Chen. (2010). Note on moderate deviations for the maximum likelihood estimator, Acta Appl. Math. 110, 863–869.


    Miao, Y. and Y. Wang. (2014). Moderate deviation principle for maximum likelihood estimator, Statistics 48, 766–777.


    Singh, S.K. and S.K. Acharya. (2019). Equivalence between Bayes and the maximum likelihood estimator in M/M/1 queue, Commun. Stat.–Theory Methods 48, 4780–4793.


    Wolff, R.W. (1965). Problems of statistical inference for birth and death queueing models, Oper. Res. 13, 243–357.


    Xiao, Z. and L. Liu. (2006). Moderate deviations of maximum likelihood estimator for independent not identically distributed case, Stat. Probab. Lett. 76, 1056–1064.

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