Adaptive Robust Confidence Bands on Local Polynomial Regression Using Residual Bootstrap Percentiles

Abstract

Ensuring reliable inference in local polynomial regression requires robust methods that can manage data irregularities, particularly outliers. This study introduces an adaptive robust approach for constructing confidence bands using residual bootstrap percentiles. Two robust weighting techniques (Huber and Tukey) were applied to address different levels of data contamination. The method was evaluated using both simulated datasets and real-world observations involving fluctuating patterns. Huber weighting produced more stable and narrower confidence bands under moderate anomalies, while Tukey weighting was more effective in handling extreme deviations. These differences arise because Huber downweights moderate residuals proportionally, whereas Tukey aggressively suppresses extreme outliers. Smoothing parameters were optimized through cross-validation to balance bias and variance effectively. This approach enhances the robustness of nonparametric regression because it maintains consistent confidence coverage despite data imperfections, offering a reliable tool for statistical inference in complex datasets.