Local Asymptotic Normality for Non-Identically Distributed Observations

Previous article Next article Local Asymptotic Normality for Non-Identically Distributed ObservationsI. A. Ibragimov and R. Z. Has’minskiiI. A. Ibragimov and R. Z. Has’minskiihttps://doi.org/10.1137/1120032PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Lucien Le Cam, Locally asymptotically normal families of distributions. Certain approximations to families of distributions and their use in the theory of estimation and testing hypotheses, Univ. california Publ. Statist., 3 (1960), 37–98 MR0126903 0104.12701 Google Scholar[2] Jaroslav Hájek, Local asymptotic minimax and admissibility in estimation, 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, 175–194 MR0400513 0281.62010 Google Scholar[3] George G. Roussas, Contiguity of probability measures: some applications in statistics, Cambridge University Press, London, 1972xiii+248 MR0359099 0265.60003 CrossrefGoogle Scholar[4] A. F. Kushnir, Asymptotically optimal tests for a regression problem of testing hypotheses, Theory Prob. Applications, 13 (1968), 647–666 10.1137/1113080 LinkGoogle Scholar[5] A. N. Philippou and , G. G. Roussas, Asymptotic distribution of the likelihood function in the independent not identically distributed case, Ann. Statist., 1 (1973), 454–471 MR0381084 0258.62011 CrossrefGoogle Scholar[6] A. M. Walker, On the estimation of a harmonic component in a time series with stationary independent residuals, Biometrika, 58 (1971), 21–36 MR0275619 0244.62064 CrossrefGoogle Scholar[7] V. F. Pisaranko, Detection of latent periodicities, International conference on the theory of probability and mathematical statistics, Summary of Proceedings, Vol. 2, Vil'nyus, 1973, 165–166, (In Russian.) Google Scholar[8] B. V. Gnedenko and , A. N. Kolmogorov, Limit distributions for sums of independent random variables, Translated from the Russian, annotated, and revised by K. L. Chung. With appendices by J. L. Doob and P. L. Hsu. Revised edition, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills., Ont., 1968ix+293 MR0233400 Google Scholar[9] I. A. Ibragimov and , R. Z. Khas'minskii˘, An estimator of the parameter of a signal in a Gaussian white noise, Problemy Peredači Informacii, 10 (1974), 39–59, (In Russian.) MR0403126 Google Scholar[10] T. W. Anderson, The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities, Proc. Amer. Math. Soc., 6 (1955), 170–176 MR0069229 0066.37402 CrossrefGoogle Scholar[11] I. I. Gikhman and , A. V. Skorokhod, Stochastic Differential Equations, Springer, New York, 1972 0242.60003 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Likelihood Ratio Processes under Nonstandard SettingsY. Goto, T. Kaneko, S. Kojima, and M. Taniguchi4 August 2022 | Theory of Probability & Its Applications, Vol. 67, No. 2AbstractPDF (438 KB)Application of convolution theorems in semiparametric models with non-i.i.d. dataJournal of Statistical Planning and Inference, Vol. 91, No. 2 Cross Ref Asymptotic Properties of Estimators for the Parameters of Spatial Inhomogeneous Poisson Point Processes1 July 2016 | Advances in Applied Probability, Vol. 26, No. 1 Cross Ref Large sample inference based on multiple observations from nonlinear autoregressive processesStochastic Processes and their Applications, Vol. 49, No. 1 Cross Ref On the Expected Amount of Information from a Non-Linear Model5 December 2018 | Journal of the Royal Statistical Society: Series B (Methodological), Vol. 54, No. 3 Cross Ref Asymptotic efficiency in estimation with conditional moment restrictionsJournal of Econometrics, Vol. 34, No. 3 Cross Ref The asymptotic distribution of the likelihood ratio for autoregressive time series with a regression trendJournal of Multivariate Analysis, Vol. 16, No. 1 Cross Ref Asymptotic Normality of Posterior Distributions Cross Ref Local asymptotic normality for progressively censored likelihood ratio statistics and applicationsJournal of Multivariate Analysis, Vol. 12, No. 2 Cross Ref On estimation and adaptive estimation for locally asymptotically normal familiesZeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 59, No. 4 Cross Ref Testing hypotheses in nonlinear regressions4 March 2011 | Series Statistics, Vol. 13, No. 1 Cross Ref Statistical estimation of nonlinear regression functions27 June 2007 | Series Statistics, Vol. 13, No. 3 Cross Ref THE COMPARISON OF LEAST SQUARES AND THIRD-ORDER PERIODOGRAM PROCEDURES IN THE ESTIMATION OF BIFREQUENCYJournal of Time Series Analysis, Vol. 1, No. 2 Cross Ref References Cross Ref On a Non-Parametric Analogue of the Information MatrixYu. A. Koshevnik and B. Ya. Levit17 July 2006 | Theory of Probability & Its Applications, Vol. 21, No. 4AbstractPDF (1546 KB)Properties of Maximum Likelihood and Bayes’ Estimators for Non-Identically Distributed ObservationsI. A. Ibragimov and R. Z. Has’minskii17 July 2006 | Theory of Probability & Its Applications, Vol. 20, No. 4AbstractPDF (757 KB)On a Problem of Testing Hypotheses and Asymptotic Normality of Stochastic IntegralsYu. A. Kutoyants17 July 2006 | Theory of Probability & Its Applications, Vol. 20, No. 2AbstractPDF (742 KB) Volume 20, Issue 2| 1976Theory of Probability & Its Applications History Submitted:30 January 1974Published online:17 July 2006 InformationCopyright © 1976 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1120032Article page range:pp. 246-260ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics