Kernel methods for optimal change-points estimation in derivatives

Ming-Yen Cheng, Marc Raimondo

Research output: Contribution to journalArticlepeer-review

Abstract

In this article we propose an implementation of the so-called zero-crossing-time detection technique specifically designed for estimating the location of jump-points in the first derivative (kinks) of a regression function f. Our algorithm relies on a new class of kernel functions having a second derivative with vanishing moments and an asymmetric first derivative steep enough near the origin. We provide a software package which, for a sample of size n, produces estimators with an accuracy of order, at least, O(n−2/5). This contrasts with current algorithms for kink estimation which at best provide an accuracy of order O(n−1/3). In the software, the kernel statistic is standardized and compared to the universal threshold to test the existence of a kink. A simulation study shows that our algorithm enjoys very good finite sample properties even for low sample sizes. The method reveal skink features in real data sets with high noise levels at places where traditional smoothers tend to over smooth the data.
Original languageEnglish
Pages (from-to)56-75
Number of pages20
JournalJournal of Computational and Graphical Statistics
Volume17
Issue number1
DOIs
Publication statusPublished - Jan 2008

User-Defined Keywords

  • Beluga whale nursing time
  • Jump-points
  • Kink
  • Legendre polynomials
  • Motorcycle data
  • Optimal rate
  • Zero-crossing time

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