Nonparametric and Tree Based Methods

该方案的研究计划分为两个部分：1）聚类/多级数据和单侧选择的非参数方法，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聚类和多层次数据的情况，聚类的一些典型例子是学校、家庭、阶层（在调查样本中）和对一个主题的重复测量。众所周知，忽略簇内相关性会导致错误的推断（通常测试和置信区间过于宽松）。 研究计划的第一部分的主要长期目标是开发非参数方法的扩展，主要是基于秩和符号的方法，用于多变量多水平数据和单侧和有序的替代品。 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，并且是非统计学家可以容易理解的工具。最近发展的集成方法，如Bagging，Boosting和随机森林，重新对这些方法的兴趣。基于树的方法主要用于处理单变量分类结果、连续结果或截尾连续结果（生存树）。然而，其他情况下的文献很少。在接下来的几年里，目标将是开发用于区间删失结果（在连续或离散尺度上测量）、用于集群右删失结果以及用于集群单变量和多变量结果（连续、分类和两者的混合）的方法。

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).