# Accession Number:

## ADA099369

# Title:

## On a Test for Multimodality Based on Kernel Density Estimates.

# Descriptive Note:

## Technical summary rept.,

# Corporate Author:

## WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

# Personal Author(s):

# Report Date:

## 1981-02-01

# Pagination or Media Count:

## 19.0

# 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

# Descriptors:

# Subject Categories:

- Statistics and Probability