Two-stage local rank estimation for generalised partially linear varying-coefficient models

This paper proposes a two-stage estimation for generalised partially linear varying-coefficient models that allow the coefficient functions to change with different covariates. By applying initial rank-based spline estimators, second-stage local rank estimators are developed to re-estimate each of the coefficient functions. The proposed two-stage estimators are shown to be asymptotically normal for both the parametric and nonparametric parts, even in scenarios with highly skewed errors or outliers, and they are able to estimate the same asymptotic distributions as accurately as if the other components were known. Via the ratios of mean-squared errors and the empirical asymptotic relative efficiency, numerical studies demonstrate that the second-stage local rank estimators perform better than the initial rank-based spline estimators. The two-stage local rank procedure is found to provide a highly efficient and robust alternative to the two-stage local least-squares or least-absolute-deviation methods. The analysis of real data also confirms the performance of the methodology.