Adaptive Robust Estimation for Varying Coefficient Models

An adaptive robust estimation framework is developed for varying coefficient models using the exponential squared loss, offering enhanced resistance to extreme observations and heavy-tailed error distributions. The methodology departs from traditional approaches that rely on a uniform smoothing parameter by employing coefficient-specific adaptive bandwidths, thereby enabling locally optimal smoothing and improving statistical efficiency. A local kernel-weighted estimation scheme combined with an iterative reweighted least squares algorithm produces a robust estimator that effectively limits the influence of outliers while preserving high efficiency under standard regularity conditions. Theoretical results establish consistency and asymptotic normality, and a data-driven procedure is introduced for selecting the tuning parameter associated with the exponential squared loss to ensure efficient performance in practice. The adaptive bandwidth mechanism further adjusts to heterogeneous smoothness patterns across coefficient functions, delivering favorable bias-variance trade-offs. Monte Carlo studies and empirical analyses based on the Boston Housing data and a real-world bike-sharing usage dataset demonstrate substantial gains in robustness, estimation accuracy, and predictive performance compared with existing competing methods.