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The weak convergence of likelihood ratio random fields and its applications. (English) Zbl 0381.62023


MSC:

62E20 Asymptotic distribution theory in statistics
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[1] Akaike, H. (1972). Information theory and an extension of the maximum likelihood principle,Proc. 2nd Int. Symp. Informations Theory, Supplement to Problems of Control and Information Theory, 267–281.
[2] Akaike, H. (1974). A new look at the statistical model identification,IEEE Trans. Automat. Contr., AC-19. · Zbl 0314.62039
[3] Bahadur, R. R. (1967). An optimal property of the likelihood ratio statistic,Proc. 5th Berkeley Symp. Math. Statist. Prob.,1, 13–26. · Zbl 0211.50901
[4] Billingsley, P. (1968).Convergence of Probability Measures, John Wiley and Sons, Inc., New York. · Zbl 0172.21201
[5] Chernoff, H. (1952). A measure of asymptotic effciency for test of a hypothesis based on the sum of observations,Ann. Math. Statist.,23, 493–507. · Zbl 0048.11804 · doi:10.1214/aoms/1177729330
[6] Huber, P. J. (1967). The behavior of maximum likelihood estimates under nonstandard conditions,Proc. 5th Berkeley Symp. Math. Statist. Prob.,1, 221–233. · Zbl 0212.21504
[7] Ibragimov, I. A. and Kha’sminskii, R. Z. (1972). Asymptotic behavior of statistical estimators in the smooth case.Theory Prob. Appl.,17, 443–460.
[8] Ibragimov, I. A. and Kha’sminskii, R. Z. (1973). Asymptotic behavior of some statistical estimators II. Limit theorems for the a posteriori density and Bayes’ estimators,Theory Prob. Appl.,18, 76–91. · Zbl 0283.62038 · doi:10.1137/1118006
[9] Inagaki, N. (1973). Asymptotic relations between the likelihood estimating function and the maximum likelihood estimator.Ann. Inst. Statist. Math.,25, 1–26. · Zbl 0332.62022 · doi:10.1007/BF02479355
[10] Inagaki, N. (1975). Akaike’s informations criterion and two errors in statistical model fitting, in preparation.
[11] Inagaki, N. and Ogata, Y. (1975). The weak convergence of the likelihood ratio random field for Markov observations,Research Memorandum, No. 79, The Institute of Statistical Mathematics. · Zbl 0381.62023
[12] LeCam, L. (1970). On the assumptions used to prove asymptotic normality of maximum likelihood estimates,Ann. Math. Statist.,41, 802–828. · Zbl 0246.62039 · doi:10.1214/aoms/1177696960
[13] Mallows, C. L. (1973). Some comments onC p Technometrics,15, 661–675. · Zbl 0269.62061 · doi:10.2307/1267380
[14] Matusita, K. (1951). On the theory of statistical decision functions,Ann. Inst. Statist. Math.,3, 17–35. · Zbl 0044.14901 · doi:10.1007/BF02949773
[15] Prokhorov, Yu. V. (1956). Convergence of random processes and limit theorems in probability theory,Theory Prob. Appl.,1, 157–214. · Zbl 0075.29001 · doi:10.1137/1101016
[16] Straf, M. L. (1970). Weak convergence of random processes with several parameters,Proc. 6th Berkeley Symp. Math. Statist. Prob.,2, 187–221.
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