Structural tests in additive regression

Abstract

We consider the component analysis problem for a regression model with an additive structure. The problem is to test if some of the additive components is of polynomial structure, e.g. linear, without specifying the structure of the remaining components. A particular case is the problem of selecting the significant covariates. The presented method is based on the wavelet transform using the Haar basis, which allows for applications under mild conditions on the design and smoothness of the regression function. The results demonstrate that each component of the model can be tested with the rate corresponding to the case if all the remaining components were known. The proposed procedure is also computationally straightforward. Simulation results and a real data example about female labor supply demonstrate the good performance of the test.