Moderate deviation for maximum likelihood estimators from single server queues
Tóm tắt
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.
Tài liệu tham khảo
Acharya, S. K.: On normal approximation for Maximum likelihood estimation from single server queues. Queueing Syst. 31, 207–216 (1999).
Acharya, S. K., Singh, S. K.: Asymptotic properties of maximum likelihood estimators from single server queues: A martingale approach. Commun. Stat. Theory Methods. 48, 3549–3557 (2019).
Basawa, I. V., Prabhu, N. U.: Estimation in single server queues. Naval. Res. Logist. Quart. 28, 475–487 (1981).
Basawa, I. V., Prabhu, N. U.: Large sample inference from single server queues. Queueing Syst. 3, 289–304 (1988).
Billingsley, P.: Statistical Inference for Markov Processes. The University of Chicago Press, Chicago (1961).
Clarke, A. B.: Maximum likelihood estimates in a simple queue. Ann. Math. Statist. 28, 1036–1040 (1957).
Cox, D. R.: Some problems of statistical analysis connected with congestion. In: Smith, W. L., Wilkinson, W. B. (eds.)Proceedings of the Symposium on Congestion Theory, pp. 289–316. University of North Carolina Press, Chapel Hill (1965).
Dembo, A., Zeitouni, O.: Large deviation Techniques and Applications. 2nd edn. Springer, New York (1998).
Ellis, R. S.: Large deviations for a general class of random vectors. Ann. Probab. 12, 1–12 (1984).
Gärtner, J: On large deviations from the invariant measure. Theory Probab. Appl. 22, 24–39 (1977).
Gao, F.: Moderate deviations for the maximum likelihood estimator. Stat. Probab. Lett. 55, 345–352 (2001).
Goyal, T. L., Harris, C. M.: Maximum likelihood estimation for queues with state dependent service. Sankhya Ser. A. 34, 65–80 (1972).
Hall, P., Heyde, C. C.: Martingale Limit Theory and Applications. Academic Press, New York (1980).
Miao, Y., Chen, Y. -X.: Note on moderate deviations for the maximum likelihood estimator. Acta Appl. Math. 110, 863–869 (2010).
Miao, Y., Wang, Y.: Moderate deviation principle for maximum likelihood estimator. Statistics. 48, 766–777 (2014).
Singh, S. K., Acharya, S. K.: Equivalence between Bayes and the maximum likelihood estimator in M/M/1 queue. Commun. Stat.–Theory Methods. 48, 4780–4793 (2019).
Wolff, R. W.: Problems of statistical inference for birth and death queueing models. Oper. Res. 13, 243–357 (1965).
Xiao, Z., Liu, L.: Moderate deviations of maximum likelihood estimator for independent not identically distributed case. Stat. Probab. Lett. 76, 1056–1064 (2006).
