Nonparametric Wavelet Regression for Binary Response

Abstract

Nonparametric regression methods have become an elegant and practical option in model building. An advantage of the nonparametric regression approach is that if a latent parametric model exists then it can be revealed by simple visual analysis of the nonparametric regression curve and selected for further analysis. This is particularly important for binary regression due to the lack of simple graphical tools for data exploration. In this article, we discuss the application of linear wavelet regression to the binary regression problem. We show that wavelet regression is consistent, attains minimax rates and is a simpler and faster alternative to generalized smooth models. As in other nonparametric smoothing problems, the choice of smoothing parameter is critical to the performance of the estimator and the appearance of the resulting estimate. In this paper, we discuss the use of a selection criterion based on Mallows’ C _L . The usefulness of the methods is explored on a real data set and in a small simulation study.

Keywords:

• Wavelets
• multiresolution analysis
• nonparametric binary regression estimation
• binning
• smoothing
• logistic regression

Corresponding author. Research supported by the IDOPT project (CNRS-INRIA-UJF-INPG).

Corresponding author. Research supported by the IDOPT project (CNRS-INRIA-UJF-INPG).

Notes

Corresponding author. Research supported by the IDOPT project (CNRS-INRIA-UJF-INPG).