Collaborative Research: 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，在方法论研究和应用的以下四个主要领域：（i）使用限制最大似然的思想开发针对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) 开发用于数量性状基因座（QTL）作图的栅栏方法； (iv) 开发用户友好的独立软件来实施栅栏方法。围栏的想法通常基于构建统计围栏或障碍，以仔细消除不正确的模型。这是通过确定哪些模型在锚定模型的拟合优度测量的变化范围内来完成的。一旦构建了栅栏，就可以根据可以灵活调整的标准从栅栏内的模型中选择最佳模型。例如，该标准可以包含科学或经济问题。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。特别令人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，研究人员计划免费传播可用的计算机软件来实施围栏方法。

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.