Power and Defect Functions of Asymptotically Efficient Tests in the Case of Markov Observed Values

Previous article Next article Power and Defect Functions of Asymptotically Efficient Tests in the Case of Markov Observed ValuesV. K. MalinovskiiV. K. Malinovskiihttps://doi.org/10.1137/1134052PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] I. Dubinskaite, Limit theorems in Rᵏ. I–III, Lithuanian Math. J., 22 (1982), 129–140, 24 (1984), pp. 256–265; pp. 325–334 0494.60024 CrossrefGoogle Scholar[2] V. V. Kalashnikov, The Qualitative Analysis of the Behavior of Complex Systems by the Method of Test Functions, Nauka, Moscow, 1978, (In Russian.) 0451.93002 Google Scholar[3] V. K. Malinovskii, On the computation of the defect of an asymptotically efficient test in the case of Markov observations, Soviet Math. Dokl., 26 (1982), 736–745 Google Scholar[4] V. K. Malinovskii, On power and defect functions of asymptotically efficient tests for Markov observed values, Stochastic Optimization, International Conference (Kiev, USSR, 1984), Summaries of Reports, Part II, Naukova Dumka, Kiev, 1984, 12–14, (In Russian.) Google Scholar[5] V. K. Malinovskii, Asymptotic optimality of tests in the problem of testing hypotheses for recurrent Markov jump processes, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 153 (1986), 105–114, 175, 179–180, (In Russian.) 88b:62160 Google Scholar[6] V. K. Malinovskii, On second-order efficiency of an asymptotically efficient test based on Markov observations, Theory Probab. Appl., 30 (1985), 603–608 10.1137/1130076 LinkGoogle Scholar[7] V. K. Malinovskii, Limit theorems for Harris Markov chains, I, Theory Probab. Appl., 31 (1986), 269–285 10.1137/1131033 LinkGoogle Scholar[8] V. K. Malinovskii, Limit theorems for Harris Markov chains, II, Theory Probab. Appl., 34 (1989), 252–265 10.1137/1134021 LinkGoogle Scholar[9] D. M. Chibisov, An asymptotic expansion for the distributions of a statistic admitting a stochastic expansion, I, II, Theory Probab. Appl., 25 (1980), 732–744, 26 (1981), pp. 1–12 10.1137/1125088 0482.62009 LinkGoogle Scholar[10] D. M. Chibisov, Calculation of the defect of asymptotically efficient tests, Theory Probab. Appl., 30 (1985), 289–310 10.1137/1130037 0593.62018 LinkGoogle Scholar[11] P. J. Bickel, , D. M. Chibisov and , W. R. van Zwet, On efficiency of first and second order, Internat. Statist. Rev., 49 (1981), 169–175 82m:62071 0469.62038 CrossrefGoogle Scholar[12] D. M. Chibisov and , W. R. van Zwet, On the Edgeworth expansions for the logarithm of the likelihood ratio, I, Theory Probab. Appl., 28 (1984), 427–451 Google Scholar[13] D. M. Chibisov, Asymptotic expansions for some asymptotically optimal tests, Proceedings of the Prague Symposium on Asymptotic Statistics (Charles Univ., Prague, 1973), Vol. II, Charles Univ., Prague, 1974, 37–68 53:4332 0361.62016 Google Scholar[14] D. M. Chibisov, Asymptotic expansions and deficiencies of tests, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983), PWN, Warsaw, 1984, 1063–1079, North-Holland/Elsevier, Amsterdam 86m:62040 0561.62021 Google Scholar[15] J. Pfanzagl, First order efficiency implies second order efficiencyContributions to statistics, Reidel, Dordrecht, 1979, 167–196, (J. Hajek Memorial Volume) 81f:62048 0427.62016 CrossrefGoogle Scholar[16] J. Pfanzagl, Asymptotic expansions in parametric statistical theoryDevelopments in statistics, Vol. 3, Academic Press, New York, 1980, 1–97 82d:62041 0481.62018 CrossrefGoogle Scholar[17] D. Revuz, Markov chains, North-Holland Publishing Co., Amsterdam, 1975x+336, Elsevier 54:3852 0332.60045 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails A renewal approach to Markovian U-statistics29 June 2011 | Mathematical Methods of Statistics, Vol. 20, No. 2 Cross Ref Asymptotic expansions in sequential estimation for the first-order random coefficient autoregressive model: Regenerative approachActa Applicandae Mathematicae, Vol. 34, No. 1-2 Cross Ref Addendum: Limit Theorems for Harris Markov Chains. IV. K. Malinovskii17 July 2006 | Theory of Probability & Its Applications, Vol. 36, No. 2PDF (92 KB) Volume 34, Issue 3| 1990Theory of Probability & Its Applications History Submitted:07 August 1986Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1134052Article page range:pp. 441-453ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics