Accession Number : ADA186037

Title :   Necessary and Sufficient Conditions for the Convergence of Integrated and Mean-Integrated r-th Order Error of Histogram Density Estimates.

Descriptive Note : Technical rept.,

Corporate Author : PITTSBURGH UNIV PA CENTER FOR MULTIVARIATE ANALYSIS

Personal Author(s) : Chen, X R ; Zhoa, L C

PDF Url : ADA186037

Report Date : Apr 1987

Pagination or Media Count : 17

Abstract : Suppose that X sub 1,...,X sub n are iid. samples drawn from a d-dimensional population with density function f. Let f(x) sub n = f sub n sub (x;X sub 1,....,X sub n) be an estimator of f(x). The Integrated Square Error (ISE) and Mean Integrated Square Error (MISE) of f sub n are important and widely used criteria in evaluating the performance of an estimator f sub n. Quite a lot of works appeared in the statistical literature dealing with the asymptotic properties of them, for various types of estimators, such as kernel estimator, orthogonal series estimator, nearest neighbor estimator etc. This paper the authors describe the necessary and sufficient conditions for the histogram estimator.

Descriptors :   *HISTOGRAMS, *CONVERGENCE, *PROBABILITY DENSITY FUNCTIONS, DENSITY, ERRORS, ESTIMATES, KERNEL FUNCTIONS, MEAN, ORTHOGONALITY

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE