Kink estimation in stochastic regression with dependent errors and predictors

TL;DR

This paper investigates the estimation of kink points in the derivative of a regression function within dependent error models, demonstrating that a zero-crossing method with high-order kernels can achieve optimal convergence rates.

Contribution

It introduces a zero-crossing based method for kink estimation in dependent data models and establishes its optimal convergence rate under certain dependence structures.

Findings

Method achieves minimax optimal rate in one model.

Convergence rate depends on dependence level and smoothness.

Applicable to models with long-range dependence.

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.