A Histogram Smoothing Estimate of the Multivariate Density Level Set

• Activity Number: 71
• Type: Contributed
• Date/Time: Monday, August 12, 2002 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics*
• Author(s): Nidhan Choudhuri*+
• Affiliation(s): Case Western Reserve University
• Keywords: density level set ; histogram smoothing ; set estimation

Abstract

Often, large scale multivariate data are encountered where it is unreasonable to assume any parametric structure. Analyzing this data requires some nonparametric tool. A commonly used approach is to study the multivariate density function generating the data through a nonparametric density estimate. A relatively newer approach is to study the density level sets through their nonparametric estimates.

This talk presents a new method of estimating multivariate density level sets, which is based on histogram smoothing of the data. This method is easy to execute, has computational advantage over the existing methods, and, thus, may be applied to fairly large data sets. This work also finds the rate of convergence of these esitmates, and the conditions required on both the level sets and the underlying density function to achieve this rate. Attention is given in finding a data-driven value of the smoothing parameter to achieve the optimal rate of convergence. The illustration of this method is then done on some two-dimensional data sets.