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Robust M-Tests

Published online by Cambridge University Press:  11 February 2009

Franco Peracchi
Franco Peracchi
Affiliation:
New York University
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Abstract

This paper investigates the local robustness properties of a general class of multidimensional tests based on M-estimators. These tests are shown to inherit the efficiency and robustness properties of the estimators on which they are based. In particular, it is shown that small perturbations of the distribution of the observations can have arbitrarily large effects on the asymptotic level and power of tests based on estimators that do not possess a bounded influence function. An asymptotic ‘admissibility’ result is also presented, which provides a justification for tests based on optimal bounded-influence estimators.

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Type
Articles
Information
Econometric Theory , Volume 7 , Issue 1 , March 1991 , pp. 69 - 84
Copyright
Copyright © Cambridge University Press 1991

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References

REFERENCES

1.Basawa, I.L. & Koul, H.L.. Large-sample statistics based on quadratic dispersion. International Statistical Review 56 (1988): 199–219.CrossRefGoogle Scholar
2.Fernholz, L.T.Von Mises Calculus for Statistical Functionals Lecture Notes in Statistics No. 19. New York: Springer, 1983.CrossRefGoogle Scholar
3.Field, C.A. & Ronchetti, E.. A tail area influence function and its application to testing. Communications in Statistics, C4 (1985): 19–41.Google Scholar
4.Foutz, R.V. & Srivastava, R.C.. The performance of the likelihood ratio test when the model is incorrect. Annals of Statistics 5 (1977): 1183–1194.CrossRefGoogle Scholar
5.Gourieroux, C. & Monfort, A.. A general theory for asymptotic tests, Document de Travail No. 8509, INSEE, Paris, 1985.Google Scholar
6.Hampel, F.R.The influence curve and its role in robust estimation. Journal of the American Statistical Association 69 (1974): 383–393.CrossRefGoogle Scholar
7.Hampel, F.R.Ronchetti, E., Rousseeuw, P.J., & Stahel, W.A.. Robust Statistics: The Approach Based on Influence Functions. New York: Wiley, 1986.Google Scholar
8.Hansen, L.P.Large sample properties of generalized method of moments estimators. Econometrica 50 (1982): 1029–1054.CrossRefGoogle Scholar
9.Hausman, J.A.Specification tests in econometrics. Econometrica 46 (1978): 1251–1272.CrossRefGoogle Scholar
10.Holly, A. Specification tests: An overview. In Bewley, T.F. (ed.), Advances in Econometrics, Fifth World Congress, Vol. 1, New York: Cambridge University Press, 1987.Google Scholar
11.Huber, P.J.Robust Statistics. New York: Wiley, 1981.CrossRefGoogle Scholar
12.Kent, J.T.Robust properties of likelihood ratio tests. Biometrika 69 (1982): 19–27.Google Scholar
13.Krasker, W.S. & Welsch, R.E.. Efficient bounded-influence regression estimation. Journal of the American Statistical Association 77 (1982): 595–604.CrossRefGoogle Scholar
14.Lambert, D.Influence function for testing. Journal of the American Statistical Association 76 (1981): 649–657.CrossRefGoogle Scholar
15.Newey, W.K.Maximum likelihood specification testing and conditional moment tests. Econometrica 53 (1985): 1047–1069.CrossRefGoogle Scholar
16.Neyman, J. Optimal asymptotic tests of composite statistical hypotheses. In Grenander, U. (ed.), Probability and Statistics: The Cramer Volume, Uppsala, Sweden: Almqvist and Wiksells, 1958.Google Scholar
17.Peracchi, F.Robust M-estimators. Econometric Reviews 9 (1990): 1–30.CrossRefGoogle Scholar
18.Rieder, H.A robust asymptotic testing model. Annals of Statistics 6 (1978): 1080–1094.CrossRefGoogle Scholar
19.Ronchetti, E. Robust testing in linear models: The infinitesimal approach, unpublished Ph.D. Thesis, ETH, Zurich, 1982.Google Scholar
20.Rousseeuw, P.J.A new infinitesimal approach to robust estimation. Zeitschrift fur Wahrscheintichkeitstheorie und verwandte Gebiete 56 (1981): 127–132.CrossRefGoogle Scholar
21.Rousseeuw, P.J. & Ronchetti, E.. Influence functions for general statistics. Journal of Computational and Applied Mathematics 7 (1981): 161–166.CrossRefGoogle Scholar
22.Schrader, R.M. & Hettmansperger, T.P.. Robust analysis of variance based upon a likelihood ratio criterion. Biometrika 67 (1980): 93–101.CrossRefGoogle Scholar
23.Serfling, R.J.Approximation Theorems of Mathematical Statistics. New York: Wiley, 1980.CrossRefGoogle Scholar
24.Vuong, Q.H.Generalized inverses and asymptotic properties of Wald tests. Economic Letters 24 (1987): 343–347.CrossRefGoogle Scholar
25.Wang, P.C.C.Robust asymptotic tests of statistical hypotheses involving nuisance parameters. Annals of Statistics 9 (1982): 1096–1106.Google Scholar