## Abstract

Two-step methods are suggested for obtaining optimal performance in the problem of estimating jump points in smooth curves. The first step is based on a kernel-type diagnostic, and the second on local least-squares. In the case of a sample of size n the exact convergence rate is n^{-1}, rather than n^{-1+δ} (for some δ > 0) in the context of recent one-step methods based purely on kernels, or n^{-1}(log n)^{1+δ} for recent techniques based on wavelets. Relatively mild assumptions are required of the error distribution. Under more stringent conditions the kernel-based step in our algorithm may be used by itself to produce an estimator with exact convergence rate n^{-1}(log n)1/2. Our techniques also enjoy good numerical performance, even in complex settings, and so offer a viable practical alternative to existing techniques, as well as providing theoretical optimality.

Original language | English |
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Pages (from-to) | 231-251 |

Number of pages | 21 |

Journal | Annals of the Institute of Statistical Mathematics |

Volume | 51 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1999 |