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Abstract: 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 singlenumber. High throughput genomic and financial data often come as rectangulararrays where each coordinate in one direction concerns subjects who might havedifferent status case or control, say, and each coordinate in the otherdesignates -outcome- for a specific feature, for example -gene,-polymorphicsite- or some aspect of financial profile. It may happen, when analyzing datathat arrive as a rectangular array, that one requires BOTH the subjects and thefeatures to be -on the same footing.- Thus there may be a need to standardizeacross rows and columns of the rectangular matrix. There arises the question asto how to achieve this double normalization. We propose and investigate theconvergence of what seems to us a natural approach to successive normalizationwhich we learned from our colleague Bradley Efron. We also study theimplementation of the method on simulated data and also on data that arose fromscientific experimentation.

Autor: Richard A. Olshen, Bala Rajaratnam


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