Statistical Models and Methods for Some Applied Problems

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The project focuses on: (1) multivariate methods based on the new concept of L1 data-depth, (2) combining classifiers with applications to biometrics measurements, (3) multivariate ordered event-time data with bias and incompleteness. All are rich areas for statistical applications and theory, where the PI's have made important contributions. In (1), the new notion of L1 depth was recently to derive a multivariate data-analytic tools, including clustering and robust regression. These tools were shown to be robust against data contamination, asymptotically efficient, and computationally "friendly" for high dimensional data. The projects extend the methods to include depth-based clustering validation, informative visualization, and multivariate linear- and nonlinear-regression based on a new concept of depth-relative-to-a-model. In (2), classification based on biometrics data is characterized by high dimensionality of objects, large number of classes, and small number of examples per class in the training data. Recent research shows that merging of classifiers can improve correct-classification rate for such problems. The project focuses on the new method of mixed group rank (MGR) combiners which is shown, based on benchmark data, to improve on the constituent as well as on other combination-methods. The project further develops MGR type combiners, establish their theoretical underpinnings, and provide the necessary computational tools to handle large data sets. In (3), multivariate ordered event-time data are common in observational studies, including epidemiology, clinical studies, behavioral studies, and more. Such data are hard to analyze, as they are typically subject to biased-sampling and censoring. A new multivariate nonparametric framework enables the extension of univariate statistical methods to multidimensional data. New statistical methods will be developed in nonparametric and semiparametric models for a variety of sampling schemes. Asymptotic (large sample) theory gives theoretical justification for the methodology.The proposed research advances several important areas in multivariate statistics. New models, methods, and algorithms will be developed for multivariate clustering, robust multivariate regression, combination of classifiers, and the analysis of biased incomplete multivariate event-time data. The proposed research has direct impact on a broad range of scientific applications outside the immediate realm of statistics. Examples include genetics studies, biometrics classification methods, epidemiological, clinical, and behavioral studies.