Monotone function estimation in partially linear models

A kernel-based method is proposed for the monotone estimation of the nonparametric function component of a partially linear regression model. The estimated monotone function is constructed via a density estimate and numerical inversion. This procedure does not require constrained optimization and hence is fast to compute. Asymptotic normality is established for the proposed monotone function estimator. We apply the proposed method to analyze mammalian eye gene expression data and reveal a complex nonlinear relation within a gene network; we also analyze the German SOEP data using our method and validate the human capital theory.