An Asymptotic Expansion for the Distribution of a Statistic Admitting an Asymptotic Expansion

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Previous article Next article An Asymptotic Expansion for the Distribution of a Statistic Admitting an Asymptotic ExpansionD. M. ChibisovD. M. Chibisovhttps://doi.org/10.1137/1117075PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. Bikjalis, Asymptotic expansions for the densities and distributions of sums of independent identically distributed random vectors, Litovsk. Mat. Sb., 8 (1968), 405–422, (In Russian.) MR0245069 (39:6381) Google Scholar[2] Yu. V. Linnik and , N. M. Mitrofanova, Some asymptotic expansions for the distribution of the maximum likelihood estimateContributions to Statistics, Statist. Publ. Soc., Calcutta, 1965, 229–238, Presented to Professor P. C. Mahalanobis MR0216621 (35:7450) 0192.25904 CrossrefGoogle Scholar[3] N. M. Mitrofanova, An asymptotic expansion for the maximum likelihood estimator for a vector parameter, Theory Prob. Applications, 12 (1967), 364–372 10.1137/1112048 0159.47803 LinkGoogle Scholar[4] D. M. Chibisov, On the normal approximation for a certain class of statistics, Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. I: Theory of statistics, Univ. California Press, Berkeley, Calif., 1972, 153–174 MR0426246 (54:14192) 0235.62011 Google Scholar[5] L. A. Lyusternik and , V. I. Sobolev, Elements of Functional Analysis, Izd-vo “Nauka”, Moscow, 1965, (In Russian.) Google Scholar[6] V. V. Yurinskii, Bounds for characteristic functions of certain degenerate multidimensional distributions, Theory Prob. Applications, 17 (1972), 101–113 10.1137/1117008 0273.60007 LinkGoogle Scholar[7] V. V. Sazanov, On the multidimensional central limit theorem, Sankhyà, A30 (1968), 181–204 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails A Higher-Order Correct Fast Moving-Average Bootstrap for Dependent DataSSRN Electronic Journal Cross Ref Asymptotic Expansion of D-Risks for Hypothesis Testing in Bernoulli Scheme17 April 2018 | Lobachevskii Journal of Mathematics, Vol. 39, No. 3 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 Contributions of Rabi Bhattacharya to the Central Limit Theory and Normal Approximation1 July 2016 Cross Ref Generalized Cordeiro–Ferrari Bartlett-type adjustmentStatistics & Probability Letters, Vol. 82, No. 11 Cross Ref Second-Order Powers of a Class of Tests in the Presence of a Nuisance ParameterCommunications in Statistics - Theory and Methods, Vol. 41, No. 20 Cross Ref Improved chi-squared tests for a composite hypothesisJournal of Multivariate Analysis, Vol. 107 Cross Ref Bibliography22 August 2011 Cross Ref Comparison of Bartlett-type adjusted tests in the multiparameter caseJournal of Multivariate Analysis, Vol. 101, No. 7 Cross Ref Second-Order Power Comparison of TestsCommunications in Statistics - Theory and Methods, Vol. 39, No. 8-9 Cross Ref Third-order power comparisons for a class of tests for multivariate linear hypothesis under general distributionsJournal of Multivariate Analysis, Vol. 100, No. 3 Cross Ref Hotelling's one-sample and two-sample T2 tests and the multivariate Behrens–Fisher problem under nonnormalityJournal of Statistical Planning and Inference, Vol. 138, No. 11 Cross Ref A comparison of higher-order local powers of a class of one-way MANOVA tests under general distributionsJournal of Multivariate Analysis, Vol. 99, No. 6 Cross Ref Asymptotic Expansions for the Distributions of Maximum and Sum of Quasi-Independent Hotelling's T2 Statistics Under Non NormalityCommunications in Statistics - Theory and Methods, Vol. 37, No. 1 Cross Ref Second-order properties of regeneration-based bootstrap for atomic Markov chains27 February 2007 | TEST, Vol. 16, No. 1 Cross Ref Moderate deviations for quadratic forms in Gaussian stationary processesJournal of Multivariate Analysis, Vol. 98, No. 5 Cross Ref Siotani’s modified second approximation for multiple comparisons of mean vectorsSUT Journal of Mathematics, Vol. 42, No. 1 Cross Ref Edgeworth expansions of suitably normalized sample mean statistics for atomic Markov chains25 May 2004 | Probability Theory and Related Fields, Vol. 130, No. 3 Cross Ref EXPANSIONS FOR THE DISTRIBUTION OF THE MAXIMUM LIKELIHOOD ESTIMATOR OF THE FRACTIONAL DIFFERENCE PARAMETER8 June 2004 | Econometric Theory, Vol. 20, No. 03 Cross Ref Edgeworth expansions for semiparametric Whittle estimation of long memoryThe Annals of Statistics, Vol. 31, No. 4 Cross Ref An Edgeworth expansion for symmetric finite population statisticsThe Annals of Probability, Vol. 30, No. 3 Cross Ref An Edgeworth expansion for symmetric statisticsThe Annals of Statistics, Vol. 25, No. 2 Cross Ref Valid Edgeworth Expansions of M-Estimators in Regression Models with Weakly Dependent Resfduals11 February 2009 | Econometric Theory, Vol. 12, No. 2 Cross Ref Edgeworth expansions for spectral mean estimates with applications to Whittle estimatesAnnals of the Institute of Statistical Mathematics, Vol. 46, No. 4 Cross Ref Chapter 39 Methodology and theory for the bootstrap Cross Ref Stochastic Expansions and Asymptotic Approximations18 October 2010 | Econometric Theory, Vol. 8, No. 3 Cross Ref The Equivalence of Two Forms of an Asymptotic ExpansionD. 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Chibisov28 July 2006 | Theory of Probability & Its Applications, Vol. 18, No. 4AbstractPDF (1116 KB)Bibliography Cross Ref Volume 17, Issue 4| 1973Theory of Probability & Its Applications History Submitted:07 October 1971Published online:28 July 2006 InformationCopyright © 1973 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1117075Article page range:pp. 620-630ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics