On the Efficiency of a Class of Non-Parametric Estimates

Previous article Next article On the Efficiency of a Class of Non-Parametric EstimatesB. Ya. LevitB. Ya. Levithttps://doi.org/10.1137/1120081PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout1 B. Levit, On optimality of some statistical estimates, Proceedings of the Prague Symposium on Asymptotic Statistics (Charles Univ., Prague, 1973), Vol. II, Charles Univ., Prague, 1974, 215–238 MR0395037 0351.62023 Google Scholar2 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 Scholar3 J. Pfanzagl, On the measurability and consistency of minimum contrast estimates, Metrika, 14 (1969), 249–272 0181.45501 CrossrefGoogle Scholar4 Peter J. Huber, Robust estimation of a location parameter, Ann. Math. Statist., 35 (1964), 73–101 MR0161415 0136.39805 CrossrefGoogle Scholar5 I. A. Ibragimov and , R. Z. Khas'minskii, Asymptotic behavior of statistical estimators in the smooth case I, II, Theory Prob. Applications, 17 (1972), 445–462, 18 (1973), pp. 76–91 10.1137/1117054 0273.62019 LinkGoogle Scholar6 L. Le Cam, On the assumptions used to prove asymptotic normality of maximum likelihood estimates, Ann. Math. Statist., 41 (1970), 802–828 MR0267676 CrossrefGoogle Scholar7 Jaroslav Hájek and , Zbyněk Šidák, Theory of rank tests, Academic Press, New York, 1967, 297– MR0229351 0161.38102 Google Scholar8 Michel Loève, Probability theory, Third edition, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1963xvi+685 MR0203748 0108.14202 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails A Modern Gauss–Markov Theorem1 January 2022 | Econometrica, Vol. 90, No. 3 Cross Ref Estimation of smooth functionals in normal models: Bias reduction and asymptotic efficiencyThe Annals of Statistics, Vol. 49, No. 5 Cross Ref Estimation of Smooth Functionals of Location Parameter in Gaussian and Poincaré Random Shift Models9 January 2021 | Sankhya A, Vol. 83, No. 2 Cross Ref Efficient estimation of smooth functionals in Gaussian shift modelsAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol. 57, No. 1 Cross Ref Assumption Lean Regression30 May 2019 | The American Statistician, Vol. 75, No. 1 Cross Ref Efficiency bounds for semiparametric models with singular score functions31 December 2019 | Econometric Reviews, Vol. 39, No. 6 Cross Ref Semiparametrically efficient estimation of Euclidean parameters under equality constraintsJournal of Statistical Planning and Inference, Vol. 201 Cross Ref Online Appendix for 'Measuring the 'Dark Matter' in Asset Pricing Models'SSRN Electronic Journal Cross Ref Double/debiased machine learning for treatment and structural parameters16 January 2018 | The Econometrics Journal, Vol. 21, No. 1 Cross Ref Research Questions in Data Science16 February 2018 Cross Ref Data-Adaptive Estimation in Cluster Randomized Trials16 February 2018 Cross Ref Higher-Order Targeted Loss-Based Estimation16 February 2018 Cross Ref Asymptotic Optimality of Estimators21 October 2017 Cross Ref Measuring the 'Dark Matter' in Asset Pricing ModelsSSRN Electronic Journal Cross Ref References9 August 2012 Cross Ref On nonparametric tests of positivity/monotonicity/convexityThe Annals of Statistics, Vol. 30, No. 2 Cross Ref An information theoretic argument for the validity of the exponential modelMetrika, Vol. 41, No. 1 Cross Ref Nonparametric estimators for Markov step processesStochastic Processes and their Applications, Vol. 52, No. 1 Cross Ref Chapter 41 Estimation of semiparametric models Cross Ref Optimal nonparametric estimation for some semimartingale stochastic differential equationsApplied Mathematics and Computation, Vol. 39, No. 3 Cross Ref Optimal nonparametric estimation for some semimartingale stochastic differential equationsApplied Mathematics and Computation, Vol. 37, No. 3 Cross Ref Semiparametric efficiency boundsJournal of Applied Econometrics, Vol. 5, No. 2 Cross Ref Large deviations and estimation in infinite-dimensional modelsStatistics & Probability Letters, Vol. 6, No. 6 Cross Ref Asymptotic efficiency in estimation with conditional moment restrictionsJournal of Econometrics, Vol. 34, No. 3 Cross Ref A characterization of limiting distributions of estimators in an autoregressive process1 December 1986 | Annals of the Institute of Statistical Mathematics, Vol. 38, No. 1 Cross Ref Asymptotic efficiency in semi-parametric models with censoringJournal of Econometrics, Vol. 32, No. 2 Cross Ref Non-parametric applications of an infinite dimensional convolution theoremZeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 68, No. 4 Cross Ref A moment estimate for rank statisticsJournal of Statistical Planning and Inference, Vol. 12 Cross Ref The minimax principle in asymptotic statistical theory27 August 2006 Cross Ref References Cross Ref On estimation and adaptive estimation for locally asymptotically normal familiesZeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 59, No. 4 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)References Cross Ref Volume 20, Issue 4| 1976Theory of Probability & Its Applications History Submitted:06 December 1973Published online:17 July 2006 InformationCopyright © 1976 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1120081Article page range:pp. 723-740ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics