JSM 2005 - Toronto

Abstract #304350

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 193
Type: Contributed
Date/Time: Monday, August 8, 2005 : 2:00 PM to 3:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #304350
Title: Stochastic Linear Hypotheses for Nonparametric Inference of High-Dimensional Data
Author(s): Jeanne Kowalski*+
Companies: Johns Hopkins University
Address: 550 North Broadway Ste 1103, Baltimore, MD, 21205, United States
Keywords: nonparametric ; u-statistics ; microarray
Abstract:

In this talk, I introduce a class of stochastic linear hypotheses to facilitate high-dimensional comparisons among several groups based on as few as a single sample per group. Unlike the classic linear hypotheses where parameters are constrained by a system of linear equations, this new class imposes a system of linear questions on a set of random vectors. Some applications of this new class of stochastic linear hypotheses are discussed within the context of analyzing high-dimensional data from few samples. In addition, the proposed theoretical framework addresses limitations of classical nonparametric tests. This class in particular includes the Mann-Whitney Wilcoxon (MWW) rank sum test as a special case. The extension of the MWW test resulted in new results in U-statistics theory for nonparametric inference for multigroup, high-dimensional data analysis. I focus on a premier application of this new class of hypotheses that motivated their development in the analyses of genomic studies involving data obtained from biotechnologies, such as microarrays.

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Revised March 2005