Fence Methods for Complex Model Selection Problems

许多模型搜索策略涉及在惩罚拟合优度度量中权衡模型拟合与模型复杂性。已经研究了回归和 ARMA 时间序列等一些常规情况下此类过程的渐近性质。然而，此类策略并不总能转化为良好的有限样本性能。此外，这种标准模型选择程序在解决非常规模型选择问题时也会遇到困难。该项目旨在开发一种新的模型选择策略，称为栅栏方法，遵循方法论研究和应用的四个主要领域：（i）使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栅栏方法；（ii）开发用于非参数模型选择问题的数据自适应栅栏方法，例如惩罚平滑样条估计； (iii) 开发用于数量性状位点 (QTL) 作图的栅栏方法；以及 (iv) 开发用于实施栅栏方法的用户友好的独立软件。栅栏的想法通常基于构建统计栅栏或屏障，以仔细消除不正确的模型。这是通过确定哪些模型在锚定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，就可以根据可以灵活调整的标准从围栏内的模型中选择最佳模型。例如，该标准可以纳入科学或经济问题。自适应栅栏方法可以被视为将信号与噪声进行比较，以得出数据支持的最佳决策。鉴于可以处理的模型如此广泛，应用范围似乎非常巨大。特别感兴趣的是在人类遗传学、医学研究和调查中的应用。为了促进此类转化研究，研究人员计划自由传播可用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.