Nonparametric wavelet regression for binary response

Nonparametric regression methods have become an elegant and practical optio n in model building. An advantage of the nonparametric regression approach is that if a latent parametric model exists then it can be revealed by simp le visual analysis of the nonparametric regression curve and selected for f urther analysis. This is particularly important for binary regression due t o the lack of simple graphical tools for data exploration. In this article, we discuss the application of linear wavelet regression to the binary regr ession problem. We show that wavelet regression is consistent, attains mini max rates and is a simpler and faster alternative to generalized smooth mod els. As in other nonparametric smoothing problems, the choice of smoothing parameter is critical to the performance of the estimator and the appearanc e of the resulting estimate. In this paper, we discuss the use of a selecti on criterion based on Mallows' CL The usefulness of the methods is explored on a real data set and in a small simulation study.