Accession Number : ADA189944
Title : Almost Sure L(Gamma)-Norm Convergence for Data-Based Histogram Density Estimates.
Descriptive Note : Technical rept. for Aug 87,
Corporate Author : PITTSBURGH UNIV PA CENTER FOR MULTIVARIATE ANALYSIS
Personal Author(s) : Zhao, L C ; Krishnaiah, P R ; Chen, X R
PDF Url : ADA189944
Report Date : Aug 1987
Pagination or Media Count : 27
Abstract : Let X1,...,Xn be i.i.d. samples drawn from a d-dimensional distribution with density f. Partition the space R subscript d into a union of disjoint intervals I sub l = I(l,X1,...,Xn) with the form I sub l = ( x = (x(1),...,x(d): - infinity a sub li or = x(i) or = b sub li infinity, i = 1,...,d). Define the database histogram estimate of f(x) based on this partition as fn(x) = The number of X1,...,Xn falling into I sub l + n times the volume of I sub l, for x is an element of I sub l, l = 1,2... For given constant r or = 1 we obtain the sufficient condition for limit as n approached infinity of the Integral over the R subscript d of the absolute value of (f sub n)(x) - f(x) to the rth power dx = O. The results give substantial improvements upon existing results. Keywords: Data based; Density estimator; Empirical distribution; Histogram.
Descriptors : *SEQUENCES(MATHEMATICS), *PROBABILITY DENSITY FUNCTIONS, DATA BASES, DENSITY, ESTIMATES, HISTOGRAMS
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE