Bootstrap-based
Bandwidth Selection for Semiparametric Generalized Regression Estimators
First
draft: 11 March 2002
This
version: 30 September 2009
Resubmitted for publication
Abstract
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This paper
considers the problem of implementing semiparametric extremum estimators of a
generalized regression model with an unknown link function. The class of estimator under consideration
includes as special cases the semiparametric least-squares estimator of
Ichimura (1993) as well as the semiparametric quasi-likelihood estimator of
Klein and Spady (1993). In general, it
is assumed to involve the computation of a nonparametric kernel estimate of
the link function that appears in place of the true, but unknown, link
function in the appropriate location in a smooth criterion function. The specific question considered in this
paper concerns the practical selection of the degree of smoothing to be used
in computing the nonparametric regression estimate. This paper proposes a method for selecting
the smoothing parameter via resampling.
The particular method suggested here involves using a resample of
smaller size than the original sample.
Specific guidance on selecting the resample size is given, and simulation
evidence is presented to illustrate the utility of this method for samples of
moderate size. |
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KEYWORDS: Bandwidth selection, semiparametric,
single-index model, bootstrap, m-out-of-n bootstrap, kernel smoothing |
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