Many model search strategies involve trading off model fit with model complexity in a penalized goodness of fit measure. Asymptotic properties for these types of procedures in some conventional situations, such as regression and ARMA time series have been studied. Yet, such strategies do not always translate into good finite sample performance. Furthermore, such standard model selection procedures encounter difficulties for nonconventional model selection problems as well. This project aims at developments of a new model selection strategy, called fence methods, in following four major areas of methodology research and applications: (i) development of adaptive fence methods for high dimensional and complex model selection problems using the idea of restricted maximum likelihood; (ii) development of data adaptive fence methods for nonparametric model selection problems such as penalized smoothing spline estimation; (iii) development of fence methods for quantitative trait loci (QTL) mapping; and (iv) development of user-friendly standalone software for implementing the fence methods.
The fence idea is generally based on building a statistical fence, or barrier, to carefully eliminate incorrect models. This is done by determining which models are within variation of a goodness-of-fit measure of an anchor model. Once the fence is constructed, the optimal model is selected from amongst those within the fence according to a criterion which can be made flexible. For example, the criterion can incorporate scientific or economic concerns. The adaptive fence method may be viewed as comparing signals with noises to come out with an optimal decision supported by the data. Given such a wide spectrum of models that can be handled, the range of applications seems enormous. Of particular interests are applications in human genetics, medical research and surveys. To facilitate such translational research, the investigators plan to freely disseminate available computer software to implement the fence methods.
