First
draft: 27 January 2009
This
version: 3 April 2009
Submitted for publication
Abstract
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This
paper is concerned with the semiparametric estimation of function means that are
scaled by an unknown conditional density function. Parameters of this form arise naturally in
the consideration of models where interest is focused on the expected value
of an integral of a conditional expectation with respect to a continuously
distributed “special regressor”' with unbounded support. In particular, a consistent and
asymptotically normal estimator of an inverse conditional density-weighted
average is proposed whose validity does not require data-dependent trimming
or the subjective choice of smoothing parameters. The asymptotic normality result is also
rate adaptive in the sense that it allows for the formulation of the usual
Wald-type inference procedures without knowledge of the estimator's actual
rate of convergence, which depends in general on the tail behaviour of the
conditional density weight. The theory
developed in this paper exploits recent results of Goh & Knight (2008)
concerning the behaviour of estimated regression-quantile residuals. Simulation experiments illustrating the
applicability of the procedure proposed here to a semiparametric
binary-choice model are suggestive of good small-sample performance. |
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KEYWORDS: Semiparametric, identification at
infinity, special regressor, rate-adaptive, regression quantile |
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