This article considers the estimation of the partially linear additive models when stochastic linear restrictions on the parametric components are available. Based on the profile least-squares approach and mixed regression estimation method, a profile mixed estimator for the parametric components is proposed and its properties are derived. Furthermore, some simulations are carried out to study the finite properties of the proposed estimator.

partially linear additive model, stochastic linear restrictions, profile least-squares, mixed regression estimator.