Hostname: page-component-7dd5485656-bt4hw Total loading time: 0 Render date: 2025-11-01T05:56:32.214Z Has data issue: false hasContentIssue false
  • English
  • Français

ASYMPTOTIC THEORY FOR ZERO ENERGYFUNCTIONALS WITH NONPARAMETRIC REGRESSIONAPPLICATIONS

Published online by Cambridge University Press:  27 August 2010

Qiying Wang  and
Peter C.B. Phillips
Get access Rights & Permissions [Opens in a new window]

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.

Information

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

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

REFERENCES

Akonom, J. (1993) Comportement asymptotique du temps d’occupation du processus des sommes partielles. Annals of the Institute of Henri Poincaré 29, 57–81.Google Scholar
Billingsley, P. (1968) Convergence of Probability Measures. Wiley.Google Scholar
Billingsley, P. (1974) Conditional distributions and tightness. Annals of Probability 2, 480–485.CrossRefGoogle Scholar
Borodin, A.N. & Ibragimov, I.A. (1995) Limit Theorems for Functionals of Random Walks. Proceedings of the Steklov Institute of Mathematics, Vol. 195 (Sudakov, V.N., ed.). American Mathematical Society.Google Scholar
Fan, J. & Gijbels, I. (1996) Local Polynomial Modeling and Its Applications. Chapman and Hall.Google Scholar
Geman, D. & Horowitz, J. (1980) Occupation densities. Annals of Probability 8, 1–67.CrossRefGoogle Scholar
Hall, P. (1977) Martingale invariance principles. Annals of Probability 5, 875–887.CrossRefGoogle Scholar
Jeganathan, P. (2004) Convergence of functionals of sums of r.v.s to local times of fractional stable motions. Annals of Probability 32, 1771–1795.CrossRefGoogle Scholar
Jeganathan, P. (2008) Limit Theorems for Functionals of Sums That Converge to Fractional Brownian and Stable Motions. Cowles Foundation Discussion Paper 1949.Google Scholar
Luklacs, E. (1970) Characteristic Functions. Hafner.Google Scholar
Petrov, V.V. (1995) Limit Theorems of Probability Theory. Oxford University Press.Google Scholar
Phillips, P.C.B. & Park, J.Y. (1998) Nonstationary Density Estimation and Kernel Autoregression. Cowles Foundation Discussion Paper 1181.Google Scholar
Wang, Q., Lin, Y.-X., & Gulati, C.M. (2003) Asymptotics for general fractionally integrated processes with applications to unit root tests. Econometric Theory 19, 143–164.CrossRefGoogle Scholar
Wang, Q. & Phillips, P.C.B. (2009a) Asymptotic theory for local time density estimation and nonparametric cointegrating regression. Econometric Theory 25, 710–738.CrossRefGoogle Scholar
Wang, Q. & Phillips, P.C.B. (2009b) Structural Nonparametric Cointegrating Regression. Econometrica 77, 1901–1948.Google Scholar