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April 2011 A two-stage hybrid procedure for estimating an inverse regression function
Runlong Tang, Moulinath Banerjee, George Michailidis
Ann. Statist. 39(2): 956-989 (April 2011). DOI: 10.1214/10-AOS820


We consider a two-stage procedure (TSP) for estimating an inverse regression function at a given point, where isotonic regression is used at stage one to obtain an initial estimate and a local linear approximation in the vicinity of this estimate is used at stage two. We establish that the convergence rate of the second-stage estimate can attain the parametric n1/2 rate. Furthermore, a bootstrapped variant of TSP (BTSP) is introduced and its consistency properties studied. This variant manages to overcome the slow speed of the convergence in distribution and the estimation of the derivative of the regression function at the unknown target quantity. Finally, the finite sample performance of BTSP is studied through simulations and the method is illustrated on a data set.


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Runlong Tang. Moulinath Banerjee. George Michailidis. "A two-stage hybrid procedure for estimating an inverse regression function." Ann. Statist. 39 (2) 956 - 989, April 2011.


Published: April 2011
First available in Project Euclid: 8 April 2011

zbMATH: 1215.62044
MathSciNet: MR2816344
Digital Object Identifier: 10.1214/10-AOS820

Primary: 62G09 , 62G20
Secondary: 62G07

Keywords: adaptive design , asymptotic properties , bootstrap , Two-stage estimator

Rights: Copyright © 2011 Institute of Mathematical Statistics


Vol.39 • No. 2 • April 2011
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