Rate of Convergence of Distributions of Maximal Deviations of Gaussian Processes and Empirical Density Functions. II

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Previous article Next article Rate of Convergence of Distributions of Maximal Deviations of Gaussian Processes and Empirical Density Functions. IIV. D. Konakov and V. I. PiterbargV. D. Konakov and V. I. Piterbarghttps://doi.org/10.1137/1128013PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] V. D. Konakov and , V. I. Piterbarg, Convergence rate of maximum deviation distributions of Gaussian processes and empirical densities, I, Theory Prob. Appl., 27 (1982), 759–779 0522.60028 LinkGoogle Scholar[2] M. Rosenblatt, Remarks on some nonparametric estimates of a density function, Ann. Math. Statist., 27 (1956), 832–837 18,159f 0073.14602 CrossrefGoogle Scholar[3] J. Komlós, , P. Major and , G. Tusnády, An approximation of partial sums of independent ${\rm RV}$'s and the sample ${\rm DF}$. I, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 32 (1975), 111–131 51:11605b 0308.60029 CrossrefGoogle Scholar[4] K. Itô and , G. McKean, Diffusion Processes and Their Sample Paths, Springer-Verlag, Berlin, 1965 0127.09503 CrossrefGoogle Scholar[5] V. D. Konakov, Complete asymptotic expansions for the maximal deviation of the empirical density function, Theory Prob. Appl., 23 (1978), 475–489 LinkGoogle Scholar[6] V. M. Alekseev, On an estimate of probability density and its derivatives, Mat. Zametki, 2 (1972), 621–626, (In Russian.) Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails On Limit Distribution of Maximal Deviation of Empirical Distribution Density and Regression Function. IIM. S. MuminovTheory of Probability & Its Applications, Vol. 56, No. 1 | 15 February 2012AbstractPDF (209 KB)On Limit Distribution of Maximal Deviation of Empirical Distribution Density and Regression Function. IM. S. MuminovTheory of Probability & Its Applications, Vol. 55, No. 3 | 7 September 2011AbstractPDF (185 KB)Confidence regions for the intensity function of a cyclic Poisson processStatistical Inference for Stochastic Processes, Vol. 12, No. 1 | 11 December 2007 Cross Ref Uniform Limit Laws for Kernel Density Estimators on Possibly Unbounded IntervalsRecent Advances in Reliability Theory | 1 Jan 2000 Cross Ref Bootstrap Confidence Regions for the Intensity of a Poisson Point ProcessJournal of the American Statistical Association, Vol. 91, No. 436 | 1 Dec 1996 Cross Ref Limit theorems for global measures of the deviation of a kernel estimate of intensity function of an inhomogeneous Poisson processJournal of Mathematical Sciences, Vol. 75, No. 2 | 1 Jun 1995 Cross Ref On the Distribution of Supremum-Type Functionals of Nonparametric Estimates of Probability and Spectral DensitiesR. RudzkisTheory of Probability & Its Applications, Vol. 37, No. 2 | 28 July 2006AbstractPDF (1091 KB)On convergence rates of supremaProbability Theory and Related Fields, Vol. 89, No. 4 | 1 Dec 1991 Cross Ref Volume 28, Issue 1| 1984Theory of Probability & Its Applications1-217 History Submitted:10 November 1978Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1128013Article page range:pp. 172-178ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics