Minimax lower bound for kink location estimators in a nonparametric regression model with long-range dependence

TL;DR

This paper establishes a fundamental lower bound for the accuracy of estimators locating kinks in a regression function's derivative within a fractional white noise model, extending previous results to models with long-range dependence.

Contribution

It introduces a minimax lower bound for kink location estimators in a nonparametric regression model with long-range dependence, filling a gap in the existing literature.

Findings

Derives a lower bound for kink estimators in fractional white noise models.

Extends minimax results to models with long-range dependence.

Provides theoretical limits for the accuracy of change point estimators.

Abstract

In this paper, a lower bound is determined in the minimax sense for change point estimators of the first derivative of a regression function in the fractional white noise model. Similar minimax results presented previously in the area focus on change points in the derivatives of a regression function in the white noise model or consider estimation of the regression function in the presence of correlated errors.