Asymptotic Expansions Associated with Some Statistical Estimators in the Smooth Case. II. Expansions of Moments and Distributions

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Previous article Next article Asymptotic Expansions Associated with Some Statistical Estimators in the Smooth Case. II. Expansions of Moments and DistributionsS. I. GusevS. I. Gusevhttps://doi.org/10.1137/1121002PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] S. I. Gusev, Asymptotic expansions associated with some statistical estimators in the smooth case, I Expansions of random variables, Theory Prob. Applications, 20 (1975), 470–498 10.1137/1120056 0359.62019 LinkGoogle Scholar[2] I. A. Ibragimov and , R. Z. Has'minskii˘, The asymptotic behavior of generalized Bayesian estimates, Dokl. Akad. Nauk SSSR, 194 (1970), 257–260, (In Russian.) MR0273724 Google Scholar[3] I. A. Ibragimov and , R. Z. Khas'minskii, Asymptotic behavior of statistical estimators in the smooth case, I. Study of the likelihood ratio, Theory Prob. Applications, 17 (1972), 445–462 10.1137/1117054 0273.62019 LinkGoogle Scholar[4] I. A. Ibragimov and , R. Z. Khas'minskii, Asymptotic behavior of some statistical estimators in the smooth case, II. Limit theorems for the a posteriors density and Bayer's estimators, Theory Prob. Applications, 18 (1973), 76–91 10.1137/1118006 0283.62038 LinkGoogle Scholar[5] D. M. Chibisov, Asymptotic expansions for statistics distributions admitting asymptotic expansions, Theory Prob. Applications, 17 (1972), , 658–688 Google Scholar[6] D. M. Chibisov, An asymptotic expansion for a class of estimators containing maximum likelihood estimators, Theory Prob. Applications, 18 (1973), 295–303 10.1137/1118031 LinkGoogle Scholar[7] D. M. Chibisov, Masters Thesis, Asymptotic Methods in Mathematical Statistics, Doctoral Dissertation, Moscow, 1972 Google Scholar[8] D. M. Chibisov, An asymptotic expansion for the distribution of sums of a special form with an application to minimum contrast estimators, Theory Prob. Applications, 18 (1973), 649–661 10.1137/1118088 0307.62014 LinkGoogle Scholar[9] Ju. V. Linnik and , N. M. Mitrofanova, On the asymptotics of the distribution of a maximum likelihood statistic, Dokl. Akad. Nauk SSSR, 149 (1963), 518–520, (In Russian.) MR0150877 Google Scholar[10] Yu. V. Linnik and , N. M. Mitrofanova, Some asymptotic expansions for the distribution of the maximum likelihood estimate, Sankhyā,Ser. A, 27 (1965), 73–82 MR0189172 0138.12901 Google Scholar[11] N. M. Mitrofanova, On the asymptotic distribution of the maximum likelihood estimate of a vector parameter, Theory Prob. Applications, 12 (1967), 364–372 10.1137/1112048 0159.47803 LinkGoogle Scholar[12] J. Pfanzagl, The Berry-Esseen bound for minimum contrast estimates, Metrika, 17 (1971), 82–91 MR0295467 0216.47805 CrossrefGoogle Scholar[13] S. I. Gusev, The asymptotic behavior of generalized a posteriori means, Dokl. Akad. Nauk SSSR, 207 (1972), 274–276, (In Russian.) MR0315821 Google Scholar[14] Dzh. Riordan, Introduction to Combinatorial Analysis, Moscow, IL, 1963 0106.24001 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Non asymptotic expansions of the MME in the case of Poisson observations8 January 2022 | Metrika, Vol. 85, No. 8 Cross Ref Asymptotic Expansion of Posterior Distribution of Parameter Centered by a n $$ \sqrt{n} $$ -Consistent Estimate22 February 2018 | Journal of Mathematical Sciences, Vol. 229, No. 6 Cross Ref Evaluating the Accuracy of Small P‐Values In Genetic Association Studies Using Edgeworth Expansions21 June 2017 | Scandinavian Journal of Statistics, Vol. 45, No. 1 Cross Ref On asymptotic expansion of posterior distribution14 July 2016 | Lobachevskii Journal of Mathematics, Vol. 37, No. 4 Cross Ref EXTREME VALUE DISTRIBUTIONS FOR BIASED SAMPLES20 January 2015 | Probability in the Engineering and Informational Sciences, Vol. 29, No. 2 Cross Ref Second-order expansion for the expected regret risk in classification of one-parametric distributionsLithuanian Mathematical Journal, Vol. 39, No. 2 Cross Ref A minimum discrepancy estimator in parameter estimationIEEE Transactions on Information Theory, Vol. 44, No. 7 Cross Ref Asymptotic expansions for the statistic and risk function of a Bayesian classification ruleJournal of Mathematical Sciences, Vol. 75, No. 2 Cross Ref Rao-Cramér Type Integral Inequalities for Estimates of a Vector ParameterA. 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