Fence Methods for Complex Model Selection Problems

许多模型搜索策略涉及在惩罚的拟合优度度量中权衡模型拟合与模型复杂性。在一些常规的情况下，如回归和阿尔马时间序列，这类程序的渐近性质进行了研究。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程序遇到困难fornonconventional模型选择问题，以及。本项目的目标是发展一种新的模型选择策略-栅栏方法，主要包括以下四个方面的方法学研究和应用：（i）利用限制极大似然的思想发展高维复杂模型选择问题的自适应栅栏方法，（ii）发展非参数模型选择问题如惩罚光滑样条估计的数据自适应栅栏方法，（iii）发展非参数模型选择问题的数据自适应栅栏方法，（iv）发展非参数模型选择问题的数据自适应栅栏方法（iii）发展数量性状基因座（QTL）定位的栅栏方法;（iv）发展用户友好的独立软件来实施栅栏方法栅栏的想法通常是建立一个统计栅栏或障碍，以仔细消除不正确的模型。这是通过确定哪些模型在锚模型的拟合优度度量的变化内来完成的。一旦栅栏被构建，根据可以灵活的标准从栅栏内的那些模型中选择最优模型。例如，该标准可以包含科学或经济方面的考虑。自适应栅栏法可以看作是将信号与噪声进行比较，以得出由数据支持的最优决策。考虑到可以处理的模型范围如此之广，应用范围似乎是巨大的。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现有的计算机软件来实施栅栏方法。

Many model search strategies involve trading off model fit with modelcomplexity in a penalized goodness of fit measure. Asymptotic propertiesfor these types of procedures in some conventional situations, such asregression and ARMA time series have been studied. Yet, such strategiesdo not always translate into good finite sample performance. Furthermore,such standard model selection procedures encounter difficulties fornonconventional model selection problems as well. This project aims atdevelopments of a new model selection strategy, called fence methods, infollowing four major areas of methodology research and applications: (i)development of adaptive fence methods for high dimensional and complexmodel selection problems using the idea of restricted maximum likelihood;(ii) development of data adaptive fence methods for nonparametric modelselection 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 implementingthe fence methods.The fence idea is generally based on building a statistical fence, orbarrier, to carefully eliminate incorrect models. This is done bydetermining which models are within variation of a goodness-of-fitmeasure of an anchor model. Once the fence is constructed, the optimalmodel is selected from amongst those within the fence according toa criterion which can be made flexible. For example, the criterion canincorporate scientific or economic concerns. The adaptive fence methodmay be viewed as comparing signals with noises to come out with an optimaldecision supported by the data. Given such a wide spectrum of models thatcan be handled, the range of applications seems enormous. Of particularinterests are applications in human genetics, medical research and surveys.To facilitate such translational research, the investigators plan to freelydisseminate available computer software to implement the fence methods.