Qu, Leming (2003), Estimating Partially Linear Models Using Wavelets: A Nonlinear Backing Algorithm, Computing Science and Statistics, 35, I2003Proceedings/QuLeming/QuLeming.paper.pdf ,
Partially linear models have a linear part as in the linear regression and a nonlinear part similar to that in the nonparametric regression. The estimates in partially linear models have been studied previously in traditional smoothing methods such as smoothing spline, kernel and piecewise polynomial methods. In this paper, we apply the regularized wavelet estimators by penalizing the $l_1$ norm of the wavelet coefficients of the nonparametric function. The regularization parameter is chosen by universal threshold. When the linear part has multivariate predictors, we developed an iterative algorithm similar to backfitting based on the necessary and sufficient conditions of the minimum point. Simulation results confirmed the good performance of the regularized wavelet approach.