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ASYMPTOTIC THEORY FOR ZERO ENERGYFUNCTIONALS WITH NONPARAMETRIC REGRESSIONAPPLICATIONS

Published online by Cambridge University Press:  27 August 2010

Qiying Wang  and
Peter C.B. Phillips
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Abstract

A local limit theorem is given for the sample mean of azero energy function of a nonstationary time seriesinvolving twin numerical sequences that pass toinfinity. The result is applicable in certainnonparametric kernel density estimation andregression problems where the relevant quantitiesare functions of both sample size and bandwidth. Aninteresting outcome of the theory in nonparametricregression is that the linear term is eliminatedfrom the asymptotic bias. In consequence and incontrast to the stationary case, the Nadaraya–Watsonestimator has the same limit distribution (to thesecond order including bias) as the local linearnonparametric estimator.

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Type
Research Article
Information
Econometric Theory , Volume 27 , Issue 2 , April 2011 , pp. 235 - 259
Copyright
Copyright © Cambridge University Press 2010

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Footnotes

Our thanks to the co-editor and two referees forhelpful comments on the original version of thispaper. Wang acknowledges partial research supportfrom the Australian Research Council. Phillipsacknowledges partial research support from the NSFunder grant SES 06-47086.

References

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