Local extremes, runs, strings and multiresolution

PL Davies, A Kovac

Research output: Contribution to journalArticle (Academic Journal)peer-review

166 Citations (Scopus)


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. tow power peaks are considered in Section 4. Section 5 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.
Translated title of the contributionLocal extremes, runs, strings and multiresolution
Original languageEnglish
Pages (from-to)1 - 48
JournalAnnals of Statistics
Volume29 (1)
Publication statusPublished - Feb 2001

Bibliographical note

Publisher: Institute of Mathematical Statistics
Other identifier: IDS Number: 445DW


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