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BIAS CORRECTIONS IN TESTING AND ESTIMATINGSEMIPARAMETRIC, SINGLE INDEX MODELS

Published online by Cambridge University Press:  17 March 2010

Roger Klein  and
Chan Shen
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Abstract

Semiparametric methods are widely employed in appliedwork where the ability to conduct inferences isimportant. To establish asymptotic normality formaking inferences, bias control mechanisms are oftenused in implementing semiparametric estimators. Thefirst contribution of this paper is to propose amechanism that enables us to establish asymptoticnormality with regular kernels. In so doing, weargue that the resulting estimator performs verywell in finite samples.

Semiparametric models are commonly estimated under asingle index assumption. Because the consistency ofthe estimator critically depends on this assumptionbeing correct, our second objective is to develop atest for it. To ensure that the test statistic hasgood size and power properties in finite samples, weemploy a bias control mechanism similar to thatunderlying the estimator. Furthermore, we structurethe test so that its form adapts to the model underthe alternative hypothesis. Monte Carlo resultsconfirm that the bias control and the adaptivefeature significantly improve the performance of thetest statistic in finite samples.

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Type
Research Article
Information
Econometric Theory , Volume 26 , Issue 6 , December 2010 , pp. 1683 - 1718
Copyright
Copyright © Cambridge University Press 2010

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Footnotes

We thank the editor and anonymous referees forhelpful comments. Any errors are the soleresponsibility of the authors.

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