Electronic Journal of Statistics

Kink estimation in stochastic regression with dependent errors and predictors

Justin Wishart and Rafał Kulik

Full-text: Open access

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 μ 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 μ. 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.

Article information

Source
Electron. J. Statist., Volume 4 (2010), 875-913.

Dates
First available in Project Euclid: 15 September 2010

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1284557752

Digital Object Identifier
doi:10.1214/10-EJS571

Mathematical Reviews number (MathSciNet)
MR2721037

Zentralblatt MATH identifier
1329.62205

Subjects
Primary: 62G08: Nonparametric regression
Secondary: 62G05: Estimation 62G20: Asymptotic properties

Keywords
Change point kink high-order kernel zero-crossing technique long-range dependence random design separation rate lemma

Citation

Wishart, Justin; Kulik, Rafał. Kink estimation in stochastic regression with dependent errors and predictors. Electron. J. Statist. 4 (2010), 875--913. doi:10.1214/10-EJS571. https://projecteuclid.org/euclid.ejs/1284557752


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