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Robust Estimation of Regression Models with Dependent Regressors: The Functional Least Squares Approach

Published online by Cambridge University Press:  18 October 2010

A. H. Welsh  and
D. F. Nicholls
A. H. Welsh
Affiliation:
University of Chicago
D. F. Nicholls
Affiliation:
Australian National University
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Abstract

In the case of regression models, one robust estimation procedure which has recently emerged is that of functional least squares. The procedure is based on the use of characteristic functions for which the tail behavior is relected by the behavior of these functions at the origin. Its attraction is that it is applicable to situations where the distribution of the disturbances may be long-tailed and/or asymmetric.

This paper extends this theory to include a large class of regression models of importance in econometrics. Indeed the regression models considered here include lagged dependent variables and deterministic exogenous variables.

Type
Research Article
Information
Econometric Theory , Volume 2 , Issue 1 , April 1986 , pp. 132 - 150
Copyright
Copyright © Cambridge University Press 1986 

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References

1. Bierens, H. J. Robust Methods and Asymptotic Theory in Non-linear Econometrics. Berlin: Springer-Verlag, 1981.Google Scholar
2. Billingsley, P. The Lindeberg-Levy theorem for martingales. Proceedings of the American Mathematical Society 12 (1961): 788–792.Google Scholar
3. Billingsley, P. Convergence of Probability Measures. New York: Wiley, 1968.Google Scholar
4. Carroll, R. J. An investigation into the effects of asymmetry of robust estimates of regression. University of North Carolina, Department of Statistics, Mimeo Series No. 1172, 1978.Google Scholar
5. Carroll, R. J. On estimating variance of robust estimators when the errors are asymmetric. Journal of the American Statistical Association 74 (1979): 674–679.Google Scholar
6. Chambers, R. L. and Heathcote, C. R.. On the estimation of slope and the identification of outliers in linear regression. Biometrika 68(1) (1981): 21–33.Google Scholar
7. Csörgö, S. The theory of functional least squares. Journal of the Australian Mathematical Society Series A 34 (1983): 336–355.Google Scholar
8. Feller, W. An Introduction to Probability Theory and Its Applications Vol. II, 2nd ed. New York: Wiley, 1971.Google Scholar
9. Feuerverger, A. and Mureika, R. A.. The empirical characteristic function and its applications. Annals of Statistics 5 (1977): 88–97.Google Scholar
10. Fiebig, D. G. and Theil, H.. Comment on robust methods in econometrics (by R. Koenker). Econometric Reviews 1 (1982): 263–270.Google Scholar
11. Heathcote, C. R. Linear regression by functional least squares. Journal of Applied Probability 19A (1982): 225–239.Google Scholar
12. Heathcote, C. R. and Welsh, A. H.. The robust estimation of autoregressive processes by functional least squares. Journal of Applied Probability 20 (1983): 737–753.Google Scholar
13. Heathcote, C. R. and Welsh, A. H.. Multivariate functional least squares. Submitted for publication (1984).Google Scholar
14. Koenker, R. Robust methods in econometrics (with discussion). Econometric Reviews 1 (1982): 213–289.Google Scholar
15. Marcus, M. B. Weak convergence of the empirical characteristic function. Annals of Probability 9 (1981): 194–201.Google Scholar
16. Rudin, W. Principles of Mathematical Analysis, 3rd ed. New York: McGraw-Hill, 1976.Google Scholar
17. Scott, D. J. Central limit theorems for martingale and for processes with stationary increments using a Skorokhod representation approach. Advances in Applied Probability 5 (1973): 119–137.Google Scholar
18. Skorokhod, A. V. Limit theorems for stochastic processes. Theory of Probability and its Applications 1 (1956): 261–290.Google Scholar
19. Welsh, A. H. An angular approach for linear data. Biometrika 72 (1985): 441–450.Google Scholar