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ASYMPTOTIC THEORY FOR ZERO ENERGY FUNCTIONALS WITH NONPARAMETRIC REGRESSION APPLICATIONS

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 a zero energy function of a nonstationary time series involving twin numerical sequences that pass to infinity. The result is applicable in certain nonparametric kernel density estimation and regression problems where the relevant quantities are functions of both sample size and bandwidth. An interesting outcome of the theory in nonparametric regression is that the linear term is eliminated from the asymptotic bias. In consequence and in contrast to the stationary case, the Nadaraya–Watson estimator has the same limit distribution (to the second order including bias) as the local linear nonparametric estimator.

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 for helpful comments on the original version of this paper. Wang acknowledges partial research support from the Australian Research Council. Phillips acknowledges partial research support from the NSF under grant SES 06-47086.

References

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