Skip to main content Accessibility help

Robust Model Selection and M-Estimation

  • José A.F. Machado (a1)

This paper studies the qualitative robustness properties of the Schwarz information criterion (SIC) based on objective functions defining M-estimators. A definition of qualitative robustness appropriate for model selection is provided and it is shown that the crucial restriction needed to achieve robustness in model selection is the uniform boundedness of the objective function. In the process, the asymptotic performance of the SIC for general M-estimators is also studied. The paper concludes with a Monte Carlo study of the finite sample behavior of the SIC for different specifications of the sample objective function.

Hide All
1.Akaike, H.A new look at the statistical model identification. IEEE Transaction on Automatic Control AC-19 (1974): 716723.
2.Billingsley, P.Convergence of Probability Measures. New York: Wiley, 1968.
3.Becker, R.A. & Chambers, J.M.. S: An Interactive Environment for Data Analysis and Graphics. Belmonte, CA: Wadsworth, 1984.
4.Geweke, J. & Meese, R.. Estimating regression models of finite but unknown order. International Economic Review 22 (1981): 5570.
5.Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J. & Stahel, W.A.. Robust Statistics: The Approach Based on Influence Functions. New York: Wiley, 1986.
6.Hildenbrand, W.Core and Equilibria of a Large Scale Economy. Princeton, NJ: Princeton University Press, 1974.
7.Huber, P.J.The behavior of maximum-likelihood estimates under nonstandard conditions. Proceedings of the Fifth Berkeley Symposium 1 (1967): 221233.
8.Huber, P.J.Robust Statistical Procedures. Philadelphia: SIAM, 1977.
9.Huber, P.J.Robust Statistics. New York: Wiley, 1981.
10.Jureckova, J. & Sen, P.K.. On adaptive scale-equivariant M-estimators. Statistics & Decisions, Supplement 1 (1984): 3146.
11.Koenker, R.W. & Bassett, G.. Regression quantiles. Econometrica 46 (1978): 3350.
12.Machado, J.A.F. Model selection: Consistency and robustness properties of the Schwarz information criterion for generalized M-estimation. Ph.D. thesis, University of Illinois, Urbana-Champaign, 1989.
13.Martin, R.D. Robust estimation of autoregressive models. In Brillinger, D.R. & Tiao, G.C. (eds.), Directions in Time Series, pp. 228262. Hayward, CA: Institute of Mathematical Statistics, 1980.
14.Ostroy, T.M. & Zame, W.R.. Non-atomic economics and the boundaries of perfect competition. Unpublished manuscript, 1987.
15.Phillips, P.C.B. & Ploberger, W.. Posterior odds testing for a unit root with data-based model selection. Cowles Foundation Discussion Paper no. 1017, 1992.
16.Poskitt, D.S. & Tremayne, A.R.. On the posterior odds in time series models. Biometrika 70 (1983): 159162.
17.Ronchetti, E.Robust model selection in regression. Statistics and Probability Letters 3 (1985): 2123.
18.Royden, H.L.Real Analysis. New York: Macmillan, 1988.
19.Schwarz, G.Estimating the dimension of a model. Annals of Statistics 6 (1978): 461464.
20.Stout, W.Almost Sure Convergence. New York: Academic Press, 1974.
21.Vuong, Q.H.Likelihood ratio tests for model selection and non-nested hypothesis. Econometrica 57 (1989): 307333.
22.White, H.Asymptotic Theory for Econometricians. Orlando, FL: Academic Press, 1984.
23.White, H. Estimation, inference, and specification analysis. Unpublished manuscript, 1988.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
  • URL: /core/journals/econometric-theory
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed