## The Annals of Statistics

### A two-stage hybrid procedure for estimating an inverse regression function

#### 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 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.

#### Article information

Source
Ann. Statist., Volume 39, Number 2 (2011), 956-989.

Dates
First available in Project Euclid: 8 April 2011

https://projecteuclid.org/euclid.aos/1302268083

Digital Object Identifier
doi:10.1214/10-AOS820

Mathematical Reviews number (MathSciNet)
MR2816344

Zentralblatt MATH identifier
1215.62044

Subjects
Primary: 62G09: Resampling methods 62G20: Asymptotic properties
Secondary: 62G07: Density estimation

#### Citation

Tang, Runlong; Banerjee, Moulinath; Michailidis, George. A two-stage hybrid procedure for estimating an inverse regression function. Ann. Statist. 39 (2011), no. 2, 956--989. doi:10.1214/10-AOS820. https://projecteuclid.org/euclid.aos/1302268083

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