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SMOOTH VARYING-COEFFICIENT ESTIMATION ANDINFERENCE FOR QUALITATIVE AND QUANTITATIVEDATA

Published online by Cambridge University Press:  17 March 2010

Qi Li  and
Jeffrey S. Racine
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Abstract

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We propose a semiparametric varying-coefficientestimator that admits both qualitative andquantitative covariates along with a test forcorrect specification of parametricvarying-coefficient models. The proposed estimatoris exceedingly flexible and has a wide range ofpotential applications including hierarchical(mixed) settings, small area estimation, etc. Adata-driven cross-validatory bandwidth selectionmethod is proposed that can handle both thequalitative and quantitative covariates and that canalso handle the presence of potentially irrelevantcovariates, each of which can result infinite-sample efficiency gains relative to theconventional frequency (sample-splitting) estimatorthat is often found in such settings. Theoreticalunderpinnings including rates of convergence andasymptotic normality are provided. Monte Carlosimulations are undertaken to assess the proposedestimator’s finite-sample performance relative tothe conventional semiparametric frequency estimatorand to assess the finite-sample performance of theproposed test for correct parametricspecification.

Information

Type
Research Article
Information
Econometric Theory , Volume 26 , Issue 6 , December 2010 , pp. 1607 - 1637
Copyright
Copyright © Cambridge University Press 2010

Footnotes

We thank a co-editor and two referees for theirvaluable comments that led to improvements in thepaper. Li’s research is partially supported by thePrivate Enterprise Research Center, Texas A&MUniversity, and the National Science Foundation ofChina (project 70773005). Racine gratefullyacknowledges support from the Natural Sciences andEngineering Research Council of Canada (NSERC:www.nserc.ca), theSocial Sciences and Humanities Research Council ofCanada (SSHRC: www.sshrc.ca), and theShared Hierarchical Academic Research ComputingNetwork (SHARCNET: www.sharcnet.ca). Racinethanks Tristen Hayfield for his exemplary researchassistance.

References

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