On a Quadratic Measure of Deviation of the Projection Estimate of a Distribution Density
É. A. Nadaraya · Theory of Probability and Its Applications · 1977
Previous article Next article On a Quadratic Measure of Deviation of the Projection Estimate of a Distribution DensityE. A. NadarayaE. A. Nadarayahttps://doi.org/10.1137/1121099PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] N. N. Chentsov, Statistical decision functions and optimal inference, Nauka, Moscow, 1972, (In Russian.) Google Scholar[2] Geoffrey S. Watson, Density estimation by orthogonal series, Ann. Math. Statist., 40 (1969), 1496–1498 MR0242332 0188.50602 CrossrefGoogle Scholar[3] Stuart C. Schwartz, Estimation of probability density by an orthogonal series, Ann. Math. Statist., 38 (1967), 1261–1265 MR0221638 0157.47904 CrossrefGoogle Scholar[4] D. Bosq, Sur l'estimation d'un densité multivariee par une série des fonctions orthogonales, C. R. Acad. Sci. Paris, 268 (1969), A555–A557 0184.42504 Google Scholar[5] Š. A. Hašimov, Estimation of a probability density by Laguerre polynomials, Random processes and statistical inference, No. 3 (Russian), Izdat. “Fan” Uzbek. SSR, Tashkent, 1973, 186–192 MR0378222 Google Scholar[6] David R. Brillinger, An asymptotic representation of the sample distribution function, Bull. Amer. Math. Soc., 75 (1969), 545–547 MR0243659 0206.20602 CrossrefGoogle Scholar[7] P. J. Bickel and , M. Rosenblatt, On some global measures of the deviations of density function estimates, Ann. Statist., 1 (1973), 1071–1095 MR0348906 0275.62033 CrossrefGoogle Scholar[8] S. S. Wilks, Collected papers: Contributions to mathematical statistics, Edited by T. W. Anderson, John Wiley & Sons Inc., New York, 1967xxvi+693 pp. (1 plate) MR0217908 Google Scholar[9] A. Zygmund, Trigonometrical Series, Izd-vo “Mir”, Moscow, 1965 0065.05604 Google Scholar[10] R. Kronmal and , M. Tarter, The estimation of probability densities and cumulatives by Fourier series methods, J. Amer. Statist. Assoc., 63 (1968), 925–952 MR0231470 0169.21403 CrossrefGoogle Scholar[11] S. Kh. Tumanyan, Asymptotic distribution of the $\chi^{2}$ criterion when the number of observations and the number of groups increase simultaneously, Theory Prob. Applications, 1 (1956), 117–131 10.1137/1101010 LinkGoogle Scholar[12] 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 MR0375412 0308.60029 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Functional Tests of Fit Cross Ref Volume 21, Issue 4| 1977Theory of Probability & Its Applications History Submitted:07 April 1975Published online:17 July 2006 InformationCopyright © 1977 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1121099Article page range:pp. 843-850ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics