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MORE EFFICIENT ESTIMATION IN NONPARAMETRIC REGRESSION WITH NONPARAMETRIC AUTOCORRELATED ERRORS

Published online by Cambridge University Press:  12 December 2005

Liangjun Su  and
Aman Ullah
Liangjun Su
Affiliation:
Guanghua School of Management, Peking University
Aman Ullah
Affiliation:
University of California, Riverside
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Abstract

We define a three-step procedure for more efficient estimation of the nonparametric regression mean with nonparametric autocorrelated errors. The procedure is based upon a nonparametric prewhitening transformation of the dependent variable that has to be estimated from the data by a local polynomial technique. We establish the asymptotic distribution of our estimator under weak dependence conditions and show that it is more efficient than the conventional local polynomial estimator. Furthermore, we consider criterion functions based on the linear exponential family, which include the local polynomial least squares criterion as a special case. Simulation evidence suggests that significant gains can be achieved in finite samples with our approach.The authors thank Oliver Linton for his many constructive and helpful suggestions. The very insightful comments from the referees are also gratefully acknowledged. The second author gratefully acknowledges financial support from the Academic Senate, UCR.

Type
Research Article
Information
Econometric Theory , Volume 22 , Issue 1 , February 2006 , pp. 98 - 126
Copyright
© 2006 Cambridge University Press

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References

REFERENCES

Andrews, D.W.K. & J.C. Monahan (1992) An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator. Econometrica 60, 953–966.CrossRefGoogle Scholar
Bosq, D. (1996) Nonparametric Statistics for Stochastic Processes: Estimation and Prediction. Lecture Notes in Statistics 110. Springer-Verlag.
Fan, J. (1992) Design-adaptive nonparametric regression. Journal of the American Statistical Association 87, 998–1004.CrossRefGoogle Scholar
Fan, J., T. Gasser, I. Gijbels, M. Brockmann, & J. Engel (1997) Local polynomial regression: Optimal kernels and asymptotic minimax efficiency. Annals of the Institute of Statistical Mathematics 49, 79–99.CrossRefGoogle Scholar
Fan, J. & I. Gijbels (1996) Local Polynomial Modelling and Its Applications. Chapman and Hall.
Gao, J. & M. King (2002) Estimation and Model Specification Testing in Nonparametric and Semiparametric Regression Models. Technical Report, Department of Mathematics and Statistics, University of Western Australia.
Gao, J. & H. Tong (2004) Semiparametric non-linear time series model selection. Journal of the Royal Statistical Society, Series B 66, 321–336.CrossRefGoogle Scholar
Gourieroux, C., A. Monfort, & A. Trognon (1984) Pseudo maximum likelihood methods: Theory. Econometrica 52, 681–700.CrossRefGoogle Scholar
Gozalo, P. & O. Linton (2000) Local non-linear least squares: Using parametric information in nonparametric regression. Journal of Econometrics 99, 63–106.CrossRefGoogle Scholar
Gozalo, P. & O. Linton (2001) Testing additivity in generalized nonparametric regression models with estimated parameters. Journal of Econometrics 104, 1–48.Google Scholar
Greene, W.H. (1997) Econometric Analysis. 3rd ed. Prentice-Hall.
Hansen, B.E. (2004) Uniform Convergence Rates for Kernel Regression. Working paper, Department of Economics, University of Wisconsin, Madison.
Hidalgo, F.J. (1992) Adaptive semiparametric estimation in the presence of autocorrelation of unknown form. Journal of Time Series Analysis 13, 47–78.CrossRefGoogle Scholar
Hong, Y. (1996) Consistent testing for serial correlation of unknown form. Econometrica 64, 837–864.CrossRefGoogle Scholar
Horowitz, J., J. Klemela, & E. Mammen (2002) Optimal estimation in additive regression models. Working paper, Northwestern University.
Li, Q. & J.M. Wooldridge (2002) Semiparametric estimation of partially linear models for dependent data with generated regressors. Econometric Theory 18, 625–645.Google Scholar
Linton, O. (1997) Efficient estimation of additive nonparametric regression models. Biometrika 84, 469–473.CrossRefGoogle Scholar
Linton, O. (2000) Efficient estimation of generalized additive nonparametric regression models. Econometric Theory 16, 502–523.CrossRefGoogle Scholar
Linton, O. & W. Härdle (1996) Estimating additive regression models with known links. Biometrika 83, 529–540.CrossRefGoogle Scholar
Masry, E. (1996a) Multivariate regression estimation: Local polynomial fitting for time series. Stochastic Processes and Their Applications 65, 81–101.Google Scholar
Masry, E. (1996b) Multivariate local polynomial regression for time series: Uniform strong consistency rates. Journal of Time Series Analysis 17, 571–599.Google Scholar
Masry, E. & D. Tjøstheim (1995) Nonparametric estimation and identification of non-linear ARCH time series. Econometric Theory 11, 258–289.CrossRefGoogle Scholar
Masry, E. & D. Tjøstheim (1997) Additive non-linear ARX time series and projection estimates. Econometric Theory 13, 214–252.CrossRefGoogle Scholar
Pagan, A. & A. Ullah (1999) Nonparametric Econometrics. Cambridge University Press.
Press, H. & J.W. Tukey (1956) Power spectral methods of analysis and their application to problems in airline dynamics. Flight Test Manual, NATO, Advisory Group for Aeronautical Research and Development, vol. IV-C, pp. 1–41.
Robinson, P.M. (1988) Root-n-consistent semiparametric regression. Econometrica 56, 931–954.CrossRefGoogle Scholar
Tong, H. (1990) Non-linear Time Series: A Dynamic Systems Approach. Oxford University Press.
Wooldridge, J.M. (2003) Introductory Econometrics: A Modern Approach. 2nd ed. South-Western.
Xiao, Z., O.B. Linton, R.J. Carroll, & E. Mammen (2003) More efficient local polynomial estimation in nonparametric regression with autocorrelated errors. Journal of the American Statistical Association 98, 980–992.CrossRefGoogle Scholar
Yao, Q. & H. Tong (1994) On subset selection in non-parametric stochastic regression. Statistica Sinica 4, 51–70.Google Scholar
Yoshihara, K. (1976) Limiting behavior of U-statistics for stationary absolutely regular processes. Zeitschrift für Wahrscheinlichskeitstheorie und Verwandte Gebiete 35, 237–252.CrossRefGoogle Scholar