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Statistical properties of the quantile normalization method for density curve alignment

Abstract : The article investigates the large sample properties of the quantile normalization method by Bolstad et al. (2003) [4] which has become one of the most popular methods to align density curves in microarray data analysis. We prove consistency of this method which is viewed as a particular case of the structural expectation procedure for curve alignment, which corresponds to a notion of barycenter of measures in the Wasserstein space. Moreover, we show that, this method fails in some case of mixtures, and we propose a new methodology to cope with this issue.
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Santiago Gallón, Jean-Michel Loubes, Elie Maza. Statistical properties of the quantile normalization method for density curve alignment. Mathematical Biosciences, Elsevier, 2013, vol. 242 (n° 2), pp. 129-142. ⟨10.1016/j.mbs.2012.12.007⟩. ⟨hal-01135106⟩

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