Open Access
February 2001 Local Extremes, Runs, Strings and Multiresolution
P. L. Davies, A. Kovac
Ann. Statist. 29(1): 1-65 (February 2001). DOI: 10.1214/aos/996986501


The paper considers the problem of nonparametric regression with emphasis on controlling the number of local extremes. Two methods, the run method and the taut-string multiresolution method, are introduced and analyzed on standard test beds. It is shown that the number and locations of local extreme values are consistently estimated. Rates of convergence are proved for both methods. The run method converges slowly but can withstand blocks as well as a high proportion of isolated outliers. The rate of convergence of the taut-string multiresolution method is almost optimal. The method is extremely sensitive and can detect very low power peaks.

Section 1 contains an introduction with special reference to the number of local extreme values. The run method is described in Section 2 and the taut-string-multiresolution method in Section 3. Low power peaks are considered in Section 4. Section contains a comparison with other methods and Section 6 a short conclusion. The proofs are given in Section 7 and the taut-string algorithm is described in the Appendix.


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P. L. Davies. A. Kovac. "Local Extremes, Runs, Strings and Multiresolution." Ann. Statist. 29 (1) 1 - 65, February 2001.


Published: February 2001
First available in Project Euclid: 5 August 2001

zbMATH: 1029.62038
MathSciNet: MR1833958
Digital Object Identifier: 10.1214/aos/996986501

Primary: 62G07
Secondary: 62G20 , 65D10

Keywords: asymptotics , local extremes , low power peaks , multiresolution analysis , Nonparametric regression , Outliers , Runs , Strings

Rights: Copyright © 2001 Institute of Mathematical Statistics

Vol.29 • No. 1 • February 2001
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