High-Dimensional Inferential Procedures under General Conditions

Document Type

Presentation Abstract

Presentation Date

4-30-2012

Abstract

In the dance of statistical academia, theory is often a step or two behind necessity. Booming advancements in technology and research over recent decades have created a need for statistical theory to address the real-life phenomena from which data so often arise. Traditionally, whether with proper justification or out of the need and desire for mathematical tractability, many assumptions are imposed in statistical methods. For instance, independence among subjects is the theoretical bedrock of the classical Central Limit Theorem first proposed over a century ago. Since that time much has changed. The aim of my research is to present inferential procedures for two-factor repeated measurements analysis of variance, both when the number of response variables is one or when it is several, and when the number of measurements taken on each subject is very large (tends to infinity). To date, there is some research relinquishing assumptions regarding the covariance structure among such data, and there are many results dealing with dependent measurements within each subject. However, to the best of our knowledge, no work has been done in both of these areas with the added relaxation of the assumption on the underlying distributional assumption. Thus far it has been assumed that the data arise from a normal or multivariate normal distribution, a condition which is dismissed in this research seeking robustness.

To those ends, this talk introduces robust, formal tests of significance along with their asymptotic distributions, and real data are analyzed to illustrate the applicability of these new methods. As an introduction, the focus will be the univariate case, that is, when the number of response variables is one. New methods are proposed which allow us to more tractably address the asymptotic nature of the test statistics. As a result, some background on the direct sum, Kronecker product, and vec matrix operators will be also be presented. A simulation discussion and an example analyzing Parkinson’s disease will be included, altogether gearing up for the presentation of the dissertation defense.

Additional Details

Monday, 30 April 2012
3:10 p.m. in Math 103
4:00 p.m. Refreshments in Math Lounge 109

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