Open Access
2010 Kink estimation in stochastic regression with dependent errors and predictors
Justin Wishart, Rafał Kulik
Electron. J. Statist. 4: 875-913 (2010). DOI: 10.1214/10-EJS571


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.


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Justin Wishart. Rafał Kulik. "Kink estimation in stochastic regression with dependent errors and predictors." Electron. J. Statist. 4 875 - 913, 2010.


Published: 2010
First available in Project Euclid: 15 September 2010

zbMATH: 1329.62205
MathSciNet: MR2721037
Digital Object Identifier: 10.1214/10-EJS571

Primary: 62G08
Secondary: 62G05 , 62G20

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

Rights: Copyright © 2010 The Institute of Mathematical Statistics and the Bernoulli Society

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