Abstract
Fence method (Jiang and others 2008. Fence methods for mixed model selection. Annals of Statistics
36, 1669-1692) is a recently proposed strategy for model selection. It was motivated by the limitation of the traditional information criteria in selecting parsimonious models in some nonconventional situations, such as mixed model selection. Jiang and others (2009. A simplified adaptive fence procedure, Statistics & Probability Letters
79, 625-629) simplified the adaptive fence method of Jiang and others (2008) to make it more suitable and convenient to use in a wide variety of problems. Still, the current modification encounters computational difficulties when applied to high-dimensional and complex problems. To address this concern, we proposed a restricted fence procedure that combines the idea of the fence with that of the restricted maximum likelihood. Furthermore, we propose to use the wild bootstrap for choosing adaptively the tuning parameter used in the restricted fence. We focus on problems of longitudinal studies and demonstrate the performance of the new procedure and its comparison with other procedures of variable selection, including the information criteria and shrinkage methods, in simulation studies. The method is further illustrated by an example of real-data analysis.