Open Access
February 2012 Nonparametric regression with homogeneous group testing data
Aurore Delaigle, Peter Hall
Ann. Statist. 40(1): 131-158 (February 2012). DOI: 10.1214/11-AOS952


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.


Download Citation

Aurore Delaigle. Peter Hall. "Nonparametric regression with homogeneous group testing data." Ann. Statist. 40 (1) 131 - 158, February 2012.


Published: February 2012
First available in Project Euclid: 15 March 2012

zbMATH: 1246.62101
MathSciNet: MR3013182
Digital Object Identifier: 10.1214/11-AOS952

Primary: 62G08

Keywords: bandwidth , local polynomial estimator , pooling , prevalence , smoothing

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 1 • February 2012
Back to Top