Nonparametric and Tree Based Methods

该方案的研究项目分为两部分：1)针对聚类/多层数据和单边方案的非参数方法，2)基于树和集成的生存、聚类和多变量数据的方法。 在实践中经常遇到涉及多层次数据的情况，一些典型的例子是学校、家庭、阶层(在调查样本中)和对某一主题的重复测量。众所周知，忽略簇内相关性会导致错误的推断(通常测试和置信度区间过于宽松)。研究计划第一部分的主要长期目标是发展非参数方法的扩展，主要是基于等级和符号的方法，用于多变量多水平数据以及单边和有序备选方案。 研究计划的第二部分的目标是为新问题开发基于树的方法。基于树的方法已经成功地应用于许多问题，是非统计学家很容易理解的工具。最近集成方法的发展，如袋装、增压和随机森林，重新引起了人们对这些方法的兴趣。基于树的方法主要被开发来处理单变量分类结果、连续结果或经审查的连续结果(生存树)。然而，对于其他情况，文献很少。在接下来的几年里，目标将是为区间审查结果(以连续或离散规模衡量)、集群右审查结果以及集群单变量和多变量结果(连续、明确和两者的混合)制定方法。

The research program of this proposal is divided into two parts: 1) Nonparametric methods for clustered/multilevel data and for one-sided alternatives, 2) Tree and ensemble based methods for survival, clustered and multivariate data. Situations involving clustered and multilevel data are often encountered in practice and some typical examples of clusters are schools, families, strata (in survey samples) and, repeated measurements on a subject. It is well-known that ignoring the intra-cluster correlation leads to erroneous inference (usually the tests and confidence intervals are too liberal). The main long term objective of the first part of the research program is to develop extensions of nonparametric methods, mostly rank and sign based methods, for multivariate multilevel data and for one-sided and ordered alternatives. The objective of the second part of the research program is to develop tree based methods for new problems. Tree based methods have been successfully applied to many problems and are tools that can be easily understood by non-statisticians. The recent development of ensemble methods, like Bagging, Boosting and Random Forests, has renewed the interest towards these methods. Tree based methods have mainly been developed to handle a univariate categorical outcome, a continuous outcome or a censored continuous outcome (survival trees). However, the literature is sparse for other situations. In the next few years, the goal will be to develop methods for an interval-censored outcome (measured on a continuous or a discrete scale), for a clustered right-censored outcome and for clustered univariate and multivariate outcomes (continuous, categorical and a mix of both).