An adaptive group LASSO approach for domain selection in functional generalized linear models

Abstract

This paper focuses on estimation and null region detection of the coefficient function for functional generalized linear models. Traditional estimating approaches cannot serve as null regions detectors. To simultaneously estimate coefficient functions and detect corresponding important subregions in functional generalized linear models, an adaptive group LASSO approach with B-spline smoothing technique is developed. The convergence rate of the resulting estimator is obtained. The consistency of domain selection and limiting distribution of the proposed estimator are then established, which is not straightforward since the groups to be penalized are overlapping. These asymptotic properties are also supported by extensive simulation studies. The resulting estimator performs better than direct adaptive LASSO estimators and some existing functional generalized linear models estimators, which are obtained without considering the domain selection. A real data application reveals the effectiveness of the proposed method.