Hao (Helen) Zhang, University of Arizona
Partial linear models provide good compromises between linear models and nonparametric models. How to determine which covariates have linear effects and which have nonlinear effects is a fundamental and theoretically challenging problem in multiple regression. Most existing methods in practice are largely ad hoc and lack theoretical justifications.
In this work, we tackle the structure selection problem from a new perspective of model selection. A unified regularization framework in reproducing kernel Hilbert space (RKHS) is developed to automatically distinguish linearity and nonlinearity of the covariates, and at the same time estimate their effects.
We show that the new estimator can discover the underlying true model structure correctly as the sample size goes to infinity. Numerical examples are given to illustrate the performance of the new procedure.
