Rank estimation of partially linear index models

We consider a generalized regression model with a partially linear index. The index contains an additive non‐parametric component in addition to the standard linear component, and the model is characterized by an unknown monotone link function. We propose weighted rank estimation procedures for estimating (a) the coefficients for the linear component, (b) the non‐parametric component (and its derivative) and (c) the average derivative for the non‐parametric component. The method is applied to study the non‐linear relationship between household income and children’s cognitive development.