We introduce new nonparametric predictors for homogeneous pooled data in the
context of group testing for rare abnormalities and show that they achieve
optimal rates of convergence. In particular, when the level of pooling is
moderate, then despite the cost savings, the method enjoys the same convergence
rate as in the case of no pooling. In the setting of "over-pooling" the
convergence rate differs from that of an optimal estimator by no more than a
logarithmic factor. Our approach improves on the random-pooling nonparametric
predictor, which is currently the only nonparametric method available, unless
there is no pooling, in which case the two approaches are identical.Comment: Published in at http://dx.doi.org/10.1214/11-AOS952 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org