login

Sequential Nonparametric Estimation of a Density

Theory of Probability and Its ApplicationsPublished 1 January 1990
S. Yu. Efroimovich
Citations30
SJR quartileQ3
SJR score0.43
SNIP0.86

Abstract

Previous article Next article Sequential Nonparametric Estimation of a DensityS. Yu. EfroimovichS. Yu. Efroimovichhttps://doi.org/10.1137/1134019PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Yu. V. Linnik and , V. I. Romanovskii, On the theory of sequential estimation, Soviet Math. Dokl., 11 (1970), 1196–1198 0232.62035 Google Scholar[2] I. A. Ibragimov and , R. Z. Khas'minskii, On sequential invariant estimation of a shift parameter, Soviet Math. Dokl., 13 (1972), 572–575 0277.62062 Google Scholar[3] I. A. Ibragimov and , R. Z. Khas'minskii, On sequential estimation, Theory Probab. Appl., 19 (1974), 233–244 10.1137/1119031 0316.62031 LinkGoogle Scholar[4] S. Yu. Efroimovich, On sequential estimation under conditions of local asymptotic normality, Theory Probab. Appl., 25 (1980), 27–40 10.1137/1125003 0467.62072 LinkGoogle Scholar[5] I. A. Ibragimov and , R. Z. Khas'minskii, Statistical estimation, Applications of Mathematics, Vol. 16, Springer-Verlag, New York, 1981vii+403, Asymptotic Theory 82g:62006 0467.62026 CrossrefGoogle Scholar[6] S. M. Ermakov, , V. Z. Brodskii and , A. A. Zhiglyavskii, The Mathematical Theory of Design of Experiments, Nauka, Moscow, 1983, (In Russian.) Google Scholar[7] N. N. Chentsov, Statistical Decision Rules and Optimal Inference, American Math. Society, Providence, RI, 1980 Google Scholar[8] E. A. Nadaraya, On the integral mean square error of some nonparametric estimates for the density function, Theory Probab. Appl., 19 (1974), 133–141 10.1137/1119010 0309.62025 LinkGoogle Scholar[9] R. Yu. Bentkus and , A. R. Kazbaras, On optimal statistical estimators of a distribution density, Soviet Math. Dokl., 23 (1981), 487–490 0501.62027 Google Scholar[10] S. Yu. Efroimovich and , M. S. Pinsker, Estimation of square-integrable probability density of a random variable, Problemy Peredachi Informatsii, 18 (1982), 19–38, (In Russian.) 85c:62093 Google Scholar[11] S. Yu. Efroimovich, Nonparametric estimation of a density of unknown smoothness, Theory Probab. Appl., 30 (1985), 557–568 10.1137/1130067 LinkGoogle Scholar[12] A. N. Shiryaev, Statistical Sequential Analysis, Nauka, Moscow, 1976, (In Russian.) 0463.62068 Google Scholar[13] R. Bentkus and , A. Kazbaras, Optimal statistical estimates of a distribution density in the presence of a priori information, Lithuanian Math. J., 22 (1982), 235–243 0535.62036 CrossrefGoogle Scholar[14] I. G. Zhurbenko, On the efficiency of spectral density estimates of a stationary process, Theory Probab. Appl., 25 (1980), 466–479 10.1137/1125059 0467.62078 LinkGoogle Scholar[15] I. A. Ibragimov and , R. Z. Khas'minskii, Bounds for the risks of nonparametric regression estimates, Theory Probab. Appl., 27 (1982), 84–89 10.1137/1127008 0508.62036 LinkGoogle Scholar[16] M. S. Pinsker, Optimal filtering of square-integrable signals on a background of Gaussian noise, Problemy Peredachi Informatsii, 16 (1980), 52–68, (In Russian.) 0452.94003 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Nonparametric bivariate density estimation for censored lifetimesThe Annals of Statistics, Vol. 50, No. 5 Cross Ref Missing, Modified, and Large- p -small- n Data in Nonparametric Curve Estimation15 May 2017 | Calcutta Statistical Association Bulletin, Vol. 69, No. 1 Cross Ref Minimax theory of nonparametric hazard rate estimation: efficiency and adaptation30 September 2014 | Annals of the Institute of Statistical Mathematics, Vol. 68, No. 1 Cross Ref Minimax Risk, Pinsker Bound for29 September 2014 Cross Ref On shrinking minimax convergence in nonparametric statistics22 July 2014 | Journal of Nonparametric Statistics, Vol. 26, No. 3 Cross Ref Nonparametric regression with responses missing at randomJournal of Statistical Planning and Inference, Vol. 141, No. 12 Cross Ref Nonparametric Regression With Predictors Missing at RandomJournal of the American Statistical Association, Vol. 106, No. 493 Cross Ref Sequential Design and Estimation in Heteroscedastic Nonparametric RegressionSequential Analysis, Vol. 26, No. 1 Cross Ref Dimension reduction in functional regression with applicationsComputational Statistics & Data Analysis, Vol. 50, No. 9 Cross Ref On Sequential Data-Driven Density EstimationSequential Analysis, Vol. 23, No. 4 Cross Ref Density estimation for biased dataThe Annals of Statistics, Vol. 32, No. 3 Cross Ref Density Estimation Under Random Censorship and Order RestrictionsJournal of the American Statistical Association, Vol. 96, No. 454 Cross Ref An overview of sequential nonparametric density estimationNonlinear Analysis: Theory, Methods & Applications, Vol. 30, No. 7 Cross Ref Density Estimation for the Case of Supersmooth Measurement ErrorJournal of the American Statistical Association, Vol. 92, No. 438 Cross Ref On nonparametric regression for IID observations in a general settingThe Annals of Statistics, Vol. 24, No. 3 Cross Ref Volume 34, Issue 2| 1990Theory of Probability & Its Applications History Submitted:01 April 1986Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1134019Article page range:pp. 228-239ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

Keywords

Computer ScienceMathematics