Local Walsh-average regression for semiparametric varying-coefficient models

This work is concerned with robust estimation in a semiparametric varying-coefficient partially linear model when the underlying error distribution deviates from a normal distribution. We develop a robust estimator by minimizing a locally Walsh-average-based loss function. We show theoretically that the proposed estimator is highly efficient across a wide spectrum of distributions. Its asymptotic relative efficiency with respect to the least-squares-based method is closely related to that of the signed-rank Wilcoxon test in comparison with the t-test. Both the theoretical and the numerical results demonstrate that the performance of the new approach is at least comparable to those of existing works.