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August 1997 Nonparametric testing of the existence of modes
Michael C. Minnotte
Ann. Statist. 25(4): 1646-1660 (August 1997). DOI: 10.1214/aos/1031594735

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.

Citation

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Michael C. Minnotte. "Nonparametric testing of the existence of modes." Ann. Statist. 25 (4) 1646 - 1660, August 1997. https://doi.org/10.1214/aos/1031594735

Information

Published: August 1997
First available in Project Euclid: 9 September 2002

zbMATH: 0936.62056
MathSciNet: MR1463568
Digital Object Identifier: 10.1214/aos/1031594735

Subjects:
Primary: 62G07, 62G10
Secondary: 62G09, 62G20

Rights: Copyright © 1997 Institute of Mathematical Statistics

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Vol.25 • No. 4 • August 1997
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