29
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Minimax sequential procedures for markov-additive processes

Pages 871-888 | Received 29 May 1997, Accepted 20 Jun 1999, Published online: 21 Mar 2007

References

  • Barndorff-Nielsen , O. 1978 . “ Information and Exponential Families ” . New York : Wiley .
  • Brown , L. 1986 . “ Fundamentals of Statistical Exponential Families IMS ” . Hayward, , CA
  • Ginlar , E. 1972 . “ Markov additive processes. I. Z. Wahrschein. verw. Gebiete ” . Vol. 24 , 85 – 93 .
  • Ezhov , I. and Skorohod , A. 1969 . Markov processes with homogeneous second component . I. Teor. Verojatn. Primen. , 14 ( 1 ) : 3 – 14 .
  • Fygenson , M. 1991 . Optimal sequential estimation for semi-Markov and Markov renewal processes . Comm. Statist. Theory Methods , 20 : 1427 – 1444 .
  • Gill , R. 1980 . Nonparametric estimation based on censored observation of a Markov renewal process . Z. Wahrschein. verw. Gebiete , 53 : 97 – 116 .
  • Magiera , R. and Stefanov , V. T. 1989 . Sequential estimation in exponential-type processes under random initial conditions . Sequential Analysis , 8 ( 2 ) : 47 – 167 .
  • Magiera , R. and Wilczyński , M. 1991 . Conjugate priors for exponential-type processes . Statistics and Probability Letters , 12 : 379 – 384 .
  • Neuts , M. 1992 . Models based on the Markovian arrival process . Ieice Trans. Commun. , E75-B ( 2 ) : 1255 – 1265 .
  • Pacheco , A. and Prabhu , N. 1995 . “ Markov-additive processes of arrivals ” . In Advances in Queueing: Theoryf Methods, and Open Problems , Edited by: Dshalalow , J. H. Vol. 6 , 167 – 194 . Boca Raton : CRC Press, Inc. .
  • Phelan , M. 1990a . Bayes estimation from a Markov renewal process . Ann. Statist , 18 ( 2 ) : 603 – 616 .
  • Phelan , M. 1990b . Estimating the transition probabilities from censored Markov renewal processes . Statist. Probab. Lett. , 10 : 43 – 47 .
  • Prabhu , N. 1991 . “ Markov renewal and Markov-additive processes ” . In Technical Report 984, College of Engineering, Cornell University
  • Rydén , T. 1994 . Parameter estimation for Markov modulated Poisson processes . Commun. Statist.-Stochastic Models , 10 ( 4 ) : 795 – 829 .
  • Stefanov , V. 1986 . Efficient sequential estimation in exponential-type processes . Ann. Statist. , 14 : 1606 – 1611 .
  • Stefanov , V. 1995 . Explicit limit results for minimal sufficient statistics and maximum likelihood estimators in some Markov processes: exponential families approach . Ann. Statist , 23 ( 4 ) : 1073 – 1101 .
  • Wilczyński , M. 1985 . Minimax sequential estimation for the multinomial and gamma processes . Zastos. Matem. , 18 ( 4 ) : 577 – 595 .

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.