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Microarray experiments provide data on the expression levels of thousands of genes and, therefore, statistical methods applicable to the analysis of such high-dimensional data are needed. In this paper, we propose robust nonparametric tools for the description and analysis of microarray data based on the concept of functional depth, which measures the centrality of an observation within a sample. We show that this concept can be easily adapted to high-dimensional observations and, in particular, to gene expression data. This allows the development of the following depth-based inference tools: (1) a scale curve for measuring and visualizing the dispersion of a set of points, (2) a rank test for deciding if 2 groups of multidimensional observations come from the same population, and (3) supervised classification techniques for assigning a new sample to one of G given groups. We apply these methods to microarray data, and to simulated data including contaminated models, and show that they are robust, efficient, and competitive with other procedures proposed in the literature, outperforming them in some situations.