|
Abstract:
|
The APLM combines the flexibility of nonparametric regression with the parsimony of regression models, and has been widely used as a popular tool in multivariate nonparametric regression to alleviate the "curse of dimensionality"'. A natural question raised in practice is the choice of structure in the nonparametric part, that is, whether the continuous covariates enter into the model in linear or nonparametric form. In this paper we present a comprehensive framework for simultaneous sparse model identification and learning for ultra-high-dimensional APLMs where both the linear and nonparametric components are possibly larger than the sample size. We propose a fast and efficient two-stage procedure, combining the tools of spline, penalty and kernels. The procedure is shown to be consistent for model structure identification. It can identify zero, linear, and nonlinear components correctly and efficiently. Inference can be made on both linear coefficients and nonparametric functions. We conduct simulation studies to evaluate the performance of the method, and apply the proposed method to a dataset on the Shoot Apical Meristem (SAM) of maize genotypes for illustration.
|
