The Annals of Statistics

Nonparametric testing of the existence of modes

Michael C. Minnotte

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Abstract

Given a set of data drawn from an unknown density, it is frequently desirable to estimate the number and location of modes of the density. A test is proposed for the weight of evidence of individual observed modes. The test statistic used is a measure of the size of the mode, the absolute integrated difference between the estimated density and the same density with the mode in question excised at the level of the higher of its two surrounding antimodes. Samples are simulated from a conservative member of the composite null hypothesis to estimate p-values within a Monte Carlo setting. Such a test can be used with the graphical "mode tree" of Minnotte and Scott to examine, in a locally adaptive fashion, not only the reality of individual modes, but also (roughly) the overall number of modes of the density. A proof of consistency of the test statistic is offered and simulation results are presented.

Article information

Source
Ann. Statist. Volume 25, Number 4 (1997), 1646-1660.

Dates
First available in Project Euclid: 9 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1031594735

Digital Object Identifier
doi:10.1214/aos/1031594735

Mathematical Reviews number (MathSciNet)
MR1463568

Zentralblatt MATH identifier
0936.62056

Subjects
Primary: 62G10: Hypothesis testing 62G07: Density estimation
Secondary: 62G09: Resampling methods 62G20: Asymptotic properties

Keywords
Bump hunting kernel density estimation mode estimation multi-modality

Citation

Minnotte, Michael C. Nonparametric testing of the existence of modes. Ann. Statist. 25 (1997), no. 4, 1646--1660. doi:10.1214/aos/1031594735. https://projecteuclid.org/euclid.aos/1031594735.


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