Nonparametric estimation of single-index models in scale-space

Abstract

Multivariate nonparametric regression faces great challenges when overburdened with large amounts of covariates. For this reason, single-index models (SIMs) have been frequently used for reducing the parameters to be estimated in nonparametric and semiparametric models. In this paper, we develop a scale-space statistical tool, known as significant zero crossings of derivatives (SiZer), for SIM. It offers the comme il faut methodology for finding important structure within data in scale-space. The average derivative is used as the coefficient vector of the SIM, which is estimated by a local-likelihood approach weighted by kernel functions. By demonstration, the proposed SiZer for the SIM successfully captures trends in simulation and in real applications. Furthermore, we provide an extension from our proposed SiZer methodology of regression to generalized linear models.