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 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 . 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.