Kink estimation in stochastic regression with dependent errors and predictors

Justin Wishart, Rafał Kulik

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.

Keywords: Change point, Kink, High-order kernel, Zero-crossing technique, Long-range dependence, Random design, Separation rate lemma.

AMS Subject Classification: Primary 62G08; secondary 62G05, 62G20.