Data Depth for Nonparametric Multivariate Analysis: Goodness-of-Fit Tests Based on Spacings, Classification, and A Coherent Framework for Data Depth

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This award is funded under the American Recovery and Reinvestment Act of 2009 Public Law 111-5). Advanced computing and data acquisition technologies have made possible the gathering of large multivariate data sets in many fields. Efficient multivariate statistical analysis tools for such data sets are highly sought after. Among the existing multivariate analysis approaches, the one based on the data depth has received most attention recently, due to its highly desirable nonparametric nature. Expanding further along the theme of data depth, this proposal outlines three new research projects in nonparametric multivariate inference, namely: (1) to develop a new class of multivariate goodness-of-fit tests based on multivariate spacings; (2) to introduce a novel nonparametric classification algorithm using the so-called DD-plots; (3) to extend the general framework for all notions of data depth, and to develop new data depths which are suitable for analyzing data drawn from non-continuous distributions. The proposal addresses important problems in theoretical multivariate statistics, which have a wide range of applications in practice. All three research directions are highly competitive, since any new development in these directions will significantly advance multivariate statistical methodology as a whole. The proposed research also aims to bring forth many efficient statistical inference procedures with immediate applicability in many domains such as medicine, biology, psychology, just to name a few. Motivating examples in ecology and environmental sciences are elaborated in the proposal. They will also be illustrated fully in future publications, which should help foster more interdisciplinary interaction between statistics and other fields.