Unified Robust Multivariate Analysis Including High-Dimensional Testing Based on Scaler Scale Analysis Kesar Singh
The goal of this proposal is to develop a general framework for multiparameter testing based on the concept of scale curves. Using a scale curve to measure the scale of a distribution, in comparison with the traditional variance-covariance matrix, has two distinct advantages: i) it provides a scalar measure and thus easier to grasp its magnitude than the complex matrix measure; and ii) the scale curve is a simple curve on the plane no matter how high the dimension of the data, and this curve can be easily visualized and interpreted. The tests proposed in this proposal are completely nonparametric and robust; and the parameters considered range from the standard ones to high-dimensional parameters pertaining to gene expression, astro-statistical and various functional data. It accomplishes the highly complex testing tasks through easy to read figures of scale bands. This scale curve based methodology can be easily comprehensible and implementable by all practitioners of statistics.
The methodology developed in this proposal will broaden substantially the application of scale curves and classical multivariate statistical analysis, while bringing down the level of technical complexities. Progress from this proposal should further the statistics discipline as a whole, and facilitate many practical applications in domains such as genetics, and risk management. For the educational purposes, the proposed research activities will allow the student to learn about modern statistics techniques such as robust multivariate analysis, the bootstrap, analysis of gene expression data, etc. Through this project, they can acquire both theoretical research skills and hands-on experience with real life data. Such training is essential for student to become contributing statisticians in the future.
