Multivariate Tests for High-Dimensional Data

• Activity Number: 296
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Guoqing Diao*+ and Bret Hanlon and Anand N. Vidyashankar
• Companies: George Mason University and University of Wisconsin-Madison and George Mason University
• Keywords: infinite dimensional framework ; joint consistency ; joint inference ; copy number ; screening

Abstract

Technical advances in biomedicine have produced an abundance of high throughput data and have stimulated substantial interest in high-dimensional two-sample problems. Recently, Kuelbs and Vidyashankar (2010, Annals of Statistics) developed an infinite-dimensional framework to study the comparisons of means when the number of parameters increase with the sample size. They demonstrate via simulations and asymptotic theory that their methods have accurate Type I error and high power. A key aspect of their approach involves estimation of the underlying covariance matrix.

In this talk , we describe an extension of their idea to more general statistical models that include regression models, logistic regression models, and proportional hazards models and provide an alternative computational methods that do not require estimation of the covariance matrix. We establish the joint consistency of our estimators and demonstrate the effectiveness of our methods using simulations in a variety of settings. We also describe how our methods can be used for screening purposes and illustrate our results in a variety of real data sets.