Mathematics – Statistics Theory
Scientific paper
2010-02-25
Annals of Statistics 2010, Vol. 38, No. 2, 1071-1093
Mathematics
Statistics Theory
Published in at http://dx.doi.org/10.1214/09-AOS736 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Scientific paper
10.1214/09-AOS736
We show that scale-adjusted versions of the centroid-based classifier enjoys optimal properties when used to discriminate between two very high-dimensional populations where the principal differences are in location. The scale adjustment removes the tendency of scale differences to confound differences in means. Certain other distance-based methods, for example, those founded on nearest-neighbor distance, do not have optimal performance in the sense that we propose. Our results permit varying degrees of sparsity and signal strength to be treated, and require only mild conditions on dependence of vector components. Additionally, we permit the marginal distributions of vector components to vary extensively. In addition to providing theory we explore numerical properties of a centroid-based classifier, and show that these features reflect theoretical accounts of performance.
Hall Peter
Pham Tung
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