SIMEX Estimation in Parametric Modal Regression with Measurement Error

TL;DR

This paper introduces a SIMEX-based estimation method for parametric modal regression models with measurement error, providing theoretical guarantees and demonstrating robustness and bias reduction through simulations.

Contribution

It proposes a novel SIMEX estimation procedure for modal regression with measurement error, with proven large sample properties and validated through simulation studies.

Findings

The estimator is consistent and asymptotically normal.

Simulation results show robustness to outliers.

The method effectively reduces bias from measurement error.

Abstract

For a class of parametric modal regression models with measurement error, a simulation extrapolation estimation procedure is proposed in this paper for estimating the modal regression coefficients. Large sample properties of the proposed estimation procedure, including the consistency and asymptotic normality, are thoroughly investigated. Simulation studies are conducted to evaluate its robustness to potential outliers and the effectiveness in reducing the bias caused by the measurement error.