Nonparametric and Tree Based Methods

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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).