Collaborative Research: Fence Methods for Complex Model Selection Problems

许多模型搜索策略涉及在拟合优度度量中权衡模型拟合和模型复杂性。研究了这类过程在一些常规情况下的渐近性质，如回归和ARMA时间序列。然而，这种策略并不总是转化为良好的有限样本性能。此外，这种标准的模型选择过程也遇到了非常规模型选择问题的困难。本项目旨在发展一种新的模型选择策略，称为围栏方法，在以下四个主要的方法论研究和应用领域：(i)利用限制最大似然的思想开发用于高维和复杂模型选择问题的自适应围栏方法；（ii）发展用于非参数模型选择问题的数据自适应栅栏方法，如惩罚平滑样条估计；(3)数量性状位点（QTL）定位的fence方法的发展；（iv）开发用户友好的独立软件来实现围栏方法。围栏概念通常基于建立统计围栏或屏障，以小心地排除不正确的模型。这是通过确定哪些模型在锚模型的拟合优度测量的变化范围内来完成的。一旦围栏建成，根据可灵活设置的标准从围栏内的模型中选择最优模型。例如，该标准可以纳入科学或经济方面的考虑。自适应围栏方法可以看作是将信号与噪声进行比较，以得到数据支持的最优决策。考虑到可以处理如此广泛的模型，应用程序的范围似乎是巨大的。特别感兴趣的是在人类遗传学、医学研究和调查中的应用。为了促进这种转化研究，研究人员计划免费传播可用的计算机软件来实现围栏方法。

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.