On a Class of Non-Parametric Estimates of Non-Linear Functionals of Density

Previous article Next article On a Class of Non-Parametric Estimates of Non-Linear Functionals of DensityYu. G. Dmitriev and F. P. TarasenkoYu. G. Dmitriev and F. P. Tarasenkohttps://doi.org/10.1137/1119045PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Murray Rosenblatt, Remarks on some nonparametric estimates of a density function, Ann. Math. Statist., 27 (1956), 832–837 MR0079873 (18,159f) 0073.14602 CrossrefGoogle Scholar[2] Emanuel Parzen, On estimation of a probability density function and mode, Ann. Math. Statist., 33 (1962), 1065–1076 MR0143282 (26:841) 0116.11302 CrossrefGoogle Scholar[3] P. K. Bhattacharya, Estimation of a probability density function and its derivatives, Sankhyā Ser. A, 29 (1967), 373–382 MR0229327 (37:4901) 0168.39703 Google Scholar[4] E. A. Nadaraya, , Trudy VTs AN Gruz. SSR, 7 (1966), 35–42, (In Georgian.) 0239.62032 Google Scholar[5] G. K. Bhattacharyya and , G. G. Roussas, Estimation of a certain functional of a probability density function, Skand. Aktuarietidskr, 1969 (1969), 201–206 (1970) MR0272130 (42:7011) 0211.50402 Google Scholar[6] Stanley C. Fralick and , Richard W. Scott, Nonparametric Bayes-risk estimation, IEEE Trans. Information Theory, IT-17 (1971), 440–444 10.1109/TIT.1971.1054663 MR0331574 (48:9906) 0241.62031 CrossrefGoogle Scholar[7] Yu. G. Dmitriev and , F. P. Tarasenko, On the estimation of functionals of the probability density and its derivatives, Theory Prob. Applications, 18 (1973), 628–633 10.1137/1118083 0301.62020 LinkGoogle Scholar[8] Wassily Hoeffding, A class of statistics with asymptotically normal distribution, Ann. Math. Statistics, 19 (1948), 293–325 MR0026294 (10,134g) 0032.04101 CrossrefGoogle Scholar[9] D. A. S. Fraser, Nonparametric methods in statistics, John Wiley & Sons Inc., New York, 1957x+299 MR0083868 (18,773d) 0077.12903 Google Scholar[10] J. L. Hodges, Jr. and , E. L. Lehmann, The efficiency of some nonparametric competitors of the t-test, Ann. Math. Statist., 27 (1956), 324–335 MR0079383 (18,78b) 0075.29206 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Exact and Asymptotically Optimal Bandwidths for Kernel Estimation of Density Functionals28 July 2011 | Methodology and Computing in Applied Probability, Vol. 14, No. 3 Cross Ref Goodness-of-fit test based on correcting moments of modified entropy estimatorJournal of Statistical Computation and Simulation, Vol. 81, No. 12 Cross Ref Density Selection and Combination Under Model Ambiguity: An Application to Stock Returns1 January 2005 | Finance and Economics Discussion Series, Vol. 2005, No. 09 Cross Ref A new estimator of entropyCommunications in Statistics - Theory and Methods, Vol. 24, No. 10 Cross Ref USING THE MUTUAL INFORMATION COEFFICIENT TO IDENTIFY LAGS IN NONLINEAR MODELSJournal of Time Series Analysis, Vol. 15, No. 4 Cross Ref Estimation of entropy and other functionals of a multivariate densityAnnals of the Institute of Statistical Mathematics, Vol. 41, No. 4 Cross Ref Semiparametric econometrics: A surveyJournal of Applied Econometrics, Vol. 3, No. 1 Cross Ref Density-free convergence properties of various estimators of entropyComputational Statistics & Data Analysis, Vol. 5, No. 4 Cross Ref On nonparametric estimation of a functional of a probability densityIEEE Transactions on Information Theory, Vol. 32, No. 1 Cross Ref References Cross Ref Volume 19, Issue 2| 1975Theory of Probability & Its Applications History Submitted:15 February 1972Published online:28 July 2006 InformationCopyright © 1975 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1119045Article page range:pp. 390-394ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics