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OPTIMAL BANDWIDTH CHOICE FOR ESTIMATION OF INVERSE CONDITIONAL–DENSITY–WEIGHTED EXPECTATIONS

Published online by Cambridge University Press:  19 June 2009

David Tomás Jacho-Chávez
David Tomás Jacho-Chávez*
Affiliation:
Indiana University
*
*Address correspondence to David T. Jacho-Chávez, Department of Economics, Indiana University, Wylie Hall 251, 100 South Woodlawn Avenue, Bloomington, IN 47405–7104, USA; e-mail: djachoch@indiana.edu.
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Abstract

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This paper characterizes the bandwidth value (h) that is optimal for estimating parameters of the form $\eta \, = \,E\left[ {\omega /f_{V|U} \left({V|U} \right)} \right]$, where the conditional density of a scalar continuous random variable V, given a random vector U, $f_{V|U} $, is replaced by its kernel estimator. That is, the parameter η is the expectation of ω inversely weighted by $f_{V|U} $, and it is the building block of various semiparametric estimators already proposed in the literature such as Lewbel (1998), Lewbel (2000b), Honoré and Lewbel (2002), Khan and Lewbel (2007), and Lewbel (2007). The optimal bandwidth is derived by minimizing the leading terms of a second-order mean squared error expansion of an in-probability approximation of the resulting estimator with respect to h. The expansion also demonstrates that the bandwidth can be chosen on the basis of bias alone, and that a simple “plug-in” estimator for the optimal bandwidth can be constructed. Finally, the small sample performance of our proposed estimator of the optimal bandwidth is assessed by a Monte Carlo experiment.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 26 , Issue 1 , February 2010, pp. 94 - 118
Copyright
Copyright © Cambridge University Press 2009

References

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