Statistical Inference in Factor Analysis for High-Dimension, Low-Sample-Size Data

• Activity Number: 518
• Type: Contributed
• Date/Time: Wednesday, August 4, 2010 : 10:30 AM to 12:20 PM
• Sponsor: ENAR
• Author(s): Miguel Marino*+ and Yi Li
• Companies: Harvard University/Dana-Farber Cancer Institute and Harvard University/Dana-Farber Cancer Institute
• Keywords: Random matrix theory ; Cancer mortality rates ; Group sequential theory ; Largest eigenvalue ; Sparse principal components ; Surveillance, epidemiology and end results program

Abstract

Cancer researchers are keen on tracking trends in cancer mortality rates and studying the cross relationship of these trends. Factor analysis which studies such cross-correlation matrices is an effective means of data reduction, whose inference typically requires the number of random variables, p, to be relatively small and fixed, and the sample size, n, to be approaching infinity. However, contemporary surveillance techniques have yielded large matrices in both dimensions, limiting the usage of existing factor analysis techniques due to the poor estimate of the covariance/correlation matrix. We develop methods, in the framework of random matrix theory, to study the cross-correlation of cancer mortality annual rate changes in the setting where p > n. Methods are implemented on SEER cancer mortality rates from 1969 through 2005.