Kink estimation in stochastic regression with dependent errors and predictors

Justin Wishart*, Rafal Kulik

*Corresponding author for this work

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this article we study the estimation of the location of jump points in the first derivative (referred to as kinks) of a regression function mu in two random design models with different long-range dependent (LRD) structures. The method is based on the zero-crossing technique and makes use of high-order kernels. The rate of convergence of the estimator is contingent on the level of dependence and the smoothness of the regression function mu. In one of the models, the convergence rate is the same as the minimax rate for kink estimation in the fixed design scenario with i.i.d. errors which suggests that the method is optimal in the minimax sense.

Original languageEnglish
Pages (from-to)875-913
Number of pages39
JournalElectronic Journal of Statistics
Volume4
DOIs
Publication statusPublished - 2010
Externally publishedYes

Keywords

  • Change point
  • kink
  • high-order kernel
  • zero-crossing technique
  • long-range dependence
  • random design
  • separation rate lemma
  • CHANGE-POINT ESTIMATION
  • TIME-SERIES REGRESSION
  • LOCAL POLYNOMIAL FITS
  • RANDOM-DESIGN
  • NONPARAMETRIC REGRESSION
  • LIMIT-THEOREMS
  • ASYMPTOTIC EQUIVALENCE
  • WAVELET REGRESSION
  • INVERSE PROBLEMS
  • MOVING AVERAGES

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