On a Test for Multimodality Based on Kernel Density Estimates.

Abstract

Kernel probability density estimates can be used to construct a test of the hypothesis that the density underlying a given univariate data set has at most k modes, for any given k greater than 1. The test is based on the critical value of the smoothing parameter for k modes to occur in the estimate. The theoretical properties of this test are investigated; the asymptotic properties of the test statistic show that the test is consistent. Furthermore the rate of convergence of the test statistic to zero gives some theoretical insight into a bootstrap technique previously suggested by the author, and also into observed properties of kernel density estimates. (Author)

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1981
Accession Number
ADA099369

Entities

People

  • B. W. Silverman

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Contracts
  • Convergence
  • Data Analysis
  • Data Science
  • Determinants (Mathematics)
  • Distribution Functions
  • Information Science
  • Mathematics
  • North Carolina
  • Probability
  • Probability Density Functions
  • Random Variables
  • Statistical Analysis
  • Statistics
  • United Kingdom
  • United States
  • Universities

Fields of Study

  • Mathematics

Readers

  • Statistical inference.