Regression estimation using surrogate responses obtained by presmoothing

Presmoothing was initially introduced in the linear regression setting as a method to improve finite sample efficiency by replacing the response variable with a nonparametric estimate of the regression function. Since then, it has found success in various domains, including survival analysis. However, the use of presmoothing with multiple continuous covariates is challenging and undesirable in practice. Inspired by the cure regression setup, we derive a simple estimator for (semi)parametric models with many regressors based on 1-dimensional presmoothing. The method is particularly valuable when the response variable is not directly observed. However, even when the response is available, presmoothing can enhance accuracy for small to moderate sample sizes. We present several applications of the proposed method in different settings and investigate its finite sample behavior through simulations.