Mathematics – Statistics Theory
Scientific paper
2010-10-04
Annals of Statistics 2010, Vol. 38, No. 3, 1638-1664
Mathematics
Statistics Theory
Published in at http://dx.doi.org/10.1214/09-AOS743 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Scientific paper
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.
Olshen Richard A.
Rajaratnam Bala
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