Forward variable selection for sparse ultra-high-dimensional generalized varying coefficient models

In this paper, we propose forward variable selection procedures for feature screening in ultra-high-dimensional generalized varying coefficient models. We employ regression spline to approximate coefficient functions and then maximize the log-likelihood to select an additional relevant covariate sequentially. If we decide we do not significantly improve the log-likelihood any more by selecting any new covariates from our stopping rule, we terminate the forward procedures and give our estimates of relevant covariates. The effect of the size of the current model has been overlooked in stopping rules for sequential procedures for high-dimensional models. Our stopping rule takes into account the size of the current model suitably. Our forward procedures have screening consistency and some other desirable properties under regularity conditions. We also present the results of numerical studies to show their good finite sample performances.