This is the program for the 2010 Joint Statistical Meetings in Vancouver, British Columbia.

Abstract Details

Activity Number: 180
Type: Contributed
Date/Time: Monday, August 2, 2010 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #307060
Title: A Two-Stage Hybrid Procedure for Estimating an Inverse Regression Function
Author(s): Runlong Tang*+ and Moulinath Banerjee and George Michailidis
Companies: University of Michigan and University of Michigan and University of Michigan
Address: 439 West Hall, Ann Arbor, MI, 48109-1107,
Keywords: two-stage ; inverse regression ; isotonic regression ; bootstrap
Abstract:

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 $n^{1/2}$ rate. Furthermore, a bootstrapped variant of TSP (BTSP) is introduced and its (strong) 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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