Performance Comparison of SIMEX and Regression Calibration for Measurement Error Correction in Nonparametric Regression

Abstract

It is well established that measurement errors in explanatory variables can result in severe attenuation bias and over-smoothing in nonparametric kernel estimation. This study compares two prominent measurement error correction procedures Simulation-Extrapolation (SIMEX) using quadratic extrapolation and Regression Calibration (RC)  against the standard, uncorrected Nadaraya–Watson (NW) estimator under classical additive error. A Monte Carlo simulation study was conducted across three sample sizes (n = 100, 200, 500) and three error variance levels ( = 0.1, 0.3, 0.5) applied to a non-linear target curve. Estimator performance was evaluated using Mean Squared Error (MSE), Mean Absolute Error (MAE) and Bias. The findings reveal a clear, complementary performance pattern supported by empirical evidence: SIMEX optimally reduces bias and MAE under low error variance ( = 0.1), achieving significant reductions in MSE compared to the uncorrected estimator, ranging from 18.1% at n = 100, to 24.0% at n = 200, and reaching up to 36.1% at n = 500. Furthermore, SIMEX reduces MAE by up to 21.0% in large sample sizes under low noise. Conversely, Regression Calibration (RC) exhibits superior stability and consistently lower overall MSE and MAE at moderate-to-severe error levels ( 0.3), offering MSE reductions of 10.3% to 14.4% across sample sizes, while avoiding the variance inflation and performance degradation inherent in SIMEX's quadratic extrapolation step under high noise. These empirical results demonstrate that selecting the optimal error correction method depends directly on the measurement error magnitude and the targeted performance metric.