Sequential Estimation of the Parameter of a Markov Chain
B. Ya. Levit, Rafail Zalmanovich Khas'minskii · Theory of Probability and Its Applications · 1974
Previous article Next article Sequential Estimation of the Parameter of a Markov ChainB. Ya. Levit and R. Z. Khas’minskiiB. Ya. Levit and R. Z. Khas’minskiihttps://doi.org/10.1137/1118068PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Yu. V. Linnik and , I. V. Romanovskii, On the theory of sequential estimation, Soviet Math. Dokl., 11 (1970), 1196–1198 0232.62035 Google Scholar[2] I. A. Ibragimov and , R. Z. Khas'minskii, On sequential invariant estimation of a shift parameter, Soviet Math. Dokl., 13 (1972), 572–575 0277.62062 Google Scholar[3] I. A. Ibragimov and , R. Z. Khas'minskii, Information inequalities and supereffective estimates, Soviet Math. Dokl., 13 (1972), 821–824 0296.62029 Google Scholar[4] J. Wolfowitz, The efficiency of sequential estimates and Wald's equation for sequential processes, Ann. Math. Statistics, 18 (1947), 215–230 MR0021288 (9,49b) 0032.04203 CrossrefGoogle Scholar[5] Michel Loève, Probability theory, Third edition, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1963xvi+685 MR0203748 (34:3596) 0108.14202 Google Scholar[6] L. Le cam, On Some Asymptotic Properties of Maximum Likelihood Estimates and Related Bayes' Estimates, University of Calif. Press, Berkeley, 1953 0052.15404 Google Scholar[7A] I. A. Ibragimov and , R. Z. Khas'minskii, Asymptotic behavior of statistical estimators in the smooth case, Theory Prob. Applications, 17 (1972), 445–462 10.1137/1117054 0273.62019 LinkGoogle Scholar[7B] I. A. Ibragimov and , R. Z. Khas'minskii, Asymptotic behavior of statistical estimators in the smooth case, Theory Prob. Applications, 18 (1973), 76–91 10.1137/1118006 0283.62038 LinkGoogle Scholar[8] J. L. Doob, Stochastic processes, John Wiley & Sons Inc., New York, 1953viii+654 MR0058896 (15,445b) 0053.26802 Google Scholar[9] Patrick Billingsley, Statistical inference for Markov processes, Statistical Research Monographs, Vol. II. The University of Chicago Press, Chicago, Ill., 1961vii+75 MR0123419 (23:A746) 0106.34201 Google Scholar[10] Harald Cramér, Mathematical Methods of Statistics, Princeton Mathematical Series, vol. 9, Princeton University Press, Princeton, N. J., 1946xvi+575 MR0016588 (8,39f) 0063.01014 Google Scholar[11] J. Borwanker, , G. Kallianpur and , B. L. S. Prakasa Rao, The Bernstein-von Mises theorem for Markov processes, Ann. Math. Statist., 42 (1971), 1241–1253 MR0298811 (45:7860) 0245.62075 CrossrefGoogle Scholar[12] D. S. Apokorin, Estimation of the parameter of a Markov process, Teoriya Informatsiyi i Upravlenie, 2 (1973), , (In Russian.) Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Volume 18, Issue 3| 1974Theory of Probability & Its Applications History Submitted:30 December 1971Published online:28 July 2006 InformationCopyright © 1974 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1118068Article page range:pp. 546-558ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics