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SMOOTH VARYING-COEFFICIENT ESTIMATION AND INFERENCE FOR QUALITATIVE AND QUANTITATIVE DATA

Published online by Cambridge University Press:  17 March 2010

Qi Li  and
Jeffrey S. Racine
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Abstract

We propose a semiparametric varying-coefficient estimator that admits both qualitative and quantitative covariates along with a test for correct specification of parametric varying-coefficient models. The proposed estimator is exceedingly flexible and has a wide range of potential applications including hierarchical (mixed) settings, small area estimation, etc. A data-driven cross-validatory bandwidth selection method is proposed that can handle both the qualitative and quantitative covariates and that can also handle the presence of potentially irrelevant covariates, each of which can result in finite-sample efficiency gains relative to the conventional frequency (sample-splitting) estimator that is often found in such settings. Theoretical underpinnings including rates of convergence and asymptotic normality are provided. Monte Carlo simulations are undertaken to assess the proposed estimator’s finite-sample performance relative to the conventional semiparametric frequency estimator and to assess the finite-sample performance of the proposed test for correct parametric specification.

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

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Footnotes

We thank a co-editor and two referees for their valuable comments that led to improvements in the paper. Li’s research is partially supported by the Private Enterprise Research Center, Texas A&M University, and the National Science Foundation of China (project 70773005). Racine gratefully acknowledges support from the Natural Sciences and Engineering Research Council of Canada (NSERC: www.nserc.ca), the Social Sciences and Humanities Research Council of Canada (SSHRC: www.sshrc.ca), and the Shared Hierarchical Academic Research Computing Network (SHARCNET: www.sharcnet.ca). Racine thanks Tristen Hayfield for his exemplary research assistance.

References

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