Accession Number : ADA288286

Title :   Fast Multidimensional Density Estimation Based on Random-width Bins.

Descriptive Note : Technical rept. no. 109,

Corporate Author : GEORGE MASON UNIV FAIRFAX VA CENTER FOR COMPUTATIONAL STATISTICS

Personal Author(s) : Hearne, Leonard B. ; Wegman, Edward J.

PDF Url : ADA288286

Report Date : OCT 1994

Pagination or Media Count : 10

Abstract : Histogram-type density estimators have some notable computational advantages over other forms of density estimation by virtue of the WARPing algorithm. However, traditional fixed-bin-width have less than satisfactory smoothing properties, being too coarse in regions of high density and too fine in regions of low density. Scott (1992) suggests the ASH algorithm as a means of overcoming these problems, but the ASH algorithm is computationally intensive somewhat negating the benefits of WARPing. Wegman (1975) proposed a variable bin-width technique for one dimensional density estimators and used sieve type methods to show strong consistency results that did not depend on smoothness properties of the underlying density. In this paper, we extend the idea to high-dimensional, variable bin-width meshes. The boundaries of the bins are determined by a random subsampling of the observations. An extension of the WARPing algorithm may still be used for fast computation. We give combinatorial arguments for calculating the number of bins and also the conditional expectation and variance of the number of observations per bin. Conditional on the random hyper-rectangular tessellation, we calculate the maximum likelihood density estimator.

Descriptors :   *ALGORITHMS, *MAXIMUM LIKELIHOOD ESTIMATION, *PROBABILITY DENSITY FUNCTIONS, COMPUTATIONS, PARAMETRIC ANALYSIS, PROBABILITY DISTRIBUTION FUNCTIONS, RANDOM VARIABLES, ANALYSIS OF VARIANCE, PROBLEM SOLVING, CONSISTENCY, MESH, STATISTICAL SAMPLES, MATHEMATICAL PROGRAMMING.

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE