Statistical properties of the quantile normalization method for density curve alignment.

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.