Open Access
June 2010 Successive normalization of rectangular arrays
Richard A. Olshen, Bala Rajaratnam
Ann. Statist. 38(3): 1638-1664 (June 2010). DOI: 10.1214/09-AOS743


Standard statistical techniques often require transforming data to have mean 0 and standard deviation 1. Typically, this process of “standardization” or “normalization” is applied across subjects when each subject produces a single number. High throughput genomic and financial data often come as rectangular arrays where each coordinate in one direction concerns subjects who might have different status (case or control, say), and each coordinate in the other designates “outcome” for a specific feature, for example, “gene,” “polymorphic site” or some aspect of financial profile. It may happen, when analyzing data that arrive as a rectangular array, that one requires BOTH the subjects and the features to be “on the same footing.” Thus there may be a need to standardize across rows and columns of the rectangular matrix. There arises the question as to how to achieve this double normalization. We propose and investigate the convergence of what seems to us a natural approach to successive normalization which we learned from our colleague Bradley Efron. We also study the implementation of the method on simulated data and also on data that arose from scientific experimentation.


Download Citation

Richard A. Olshen. Bala Rajaratnam. "Successive normalization of rectangular arrays." Ann. Statist. 38 (3) 1638 - 1664, June 2010.


Published: June 2010
First available in Project Euclid: 24 March 2010

zbMATH: 1189.62109
MathSciNet: MR2662355
Digital Object Identifier: 10.1214/09-AOS743

Primary: 60F15 , 60G46 , 62H05

Keywords: backwards martingale convergence theorem , normalization , standardization

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.38 • No. 3 • June 2010
Back to Top