## Robust estimators for simultaneous equations models.(English)Zbl 0900.62652

Summary: This paper presents a class of robust estimators for linear and non-linear simultaneous equations models, which are a direct generalization of the maximum likelihood estimator. The new estimators are obtained as solutions of a generalized likelihood equation. They are resistant to deviations from the model distribution, to outlying observations, and to some model misspecifications. An optimality principle leads to the construction of an optimal robust estimator which is the best trade-off between efficiency at the model and robustness.

### MSC:

 62P20 Applications of statistics to economics

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### References:

 [1] Amemiya, T., The maximum likelihood and the nonlinear simultaneous equation model, Econometrica, 45, 955-968 (1977) · Zbl 0359.62026 [2] Amemiya, T., Two stage least absolute deviations estimators, Econometrica, 50, 689-711 (1982) · Zbl 0493.62098 [3] Chow, G. C., Econometrics (1983), McGraw-Hill: McGraw-Hill New York [4] Duncan, G. M., A simplified approach to $$M$$-estimation with application to two-stage estimators, Journal of Econometrics, 34, 373-389 (1987) · Zbl 0612.62027 [5] Hampel, F. R., Contributions to the theory of robust estimation, (Ph.D. thesis (1968), University of California: University of California Berkeley) [6] Hampel, F. R., The influence curve and its role in robust estimation, Journal of the American Statistical Association, 69, 383-393 (1974) · Zbl 0305.62031 [7] Hampel, F. R.; Ronchetti, E. M.; Rousseeuw, P. J.; Stahel, W. A., Robust statistics: The approach based on influence functions (1986), Wiley: Wiley New York · Zbl 0593.62027 [8] Heritier, S.; Ronchetti, E., Robust bounded-influence tests in general parametric models, Journal of the American Statistical Association, 89, 897-904 (1994) · Zbl 0804.62037 [9] Huber, P. J., The behavior of maximum likelihood estimates under nonstandard conditions, (Proceedings of the 5th Berkeley symposium on mathematical statistics and probability, Vol. 1 (1967)), 221-233 · Zbl 0212.21504 [10] Huber, P. J., Robust statistics (1981), Wiley: Wiley New York · Zbl 0536.62025 [11] Koenker, R. W., Robust methods in econometrics, Econometric Review, 1, 213-255 (1982) · Zbl 0512.62111 [12] Koenker, R. W.; Bassett, G., Regression quantiles, Econometrica, 46, 33-50 (1978) · Zbl 0373.62038 [13] Koenker, R. W.; Portnoy, S., $$M$$-estimation of multivariate regressions, Journal of the American Statistical Association, 85, 1060-1068 (1990) · Zbl 0743.62056 [14] Krasker, W. S., Parametric estimation in approximate parametric models (1977), manuscript [15] Krasker, W. S., Two-stage bounded-influence estimators for simultaneous-equations models, Journal of Business and Economic Statistics, 4, 437-444 (1986) [16] Krasker, W. S.; Welsch, R. E., Efficient bounded-influence regression estimation, Journal of the American Statistical Association, 77, 595-604 (1982) · Zbl 0501.62062 [17] Krasker, W. S.; Welsch, R. E., Resistant estimation for simultaneous-equations models using weighted instrumental variables, Econometrica, 53, 1475-1488 (1985) · Zbl 0583.62095 [18] Markatou, M.; Stahel, W. A.; Ronchetti, E., Robust $$M$$-type testing procedures for linear models, (Stahel, W. A.; Weisberg, S., Directions in robust statistics and diagnostics: Part I, IMA Volumes in Mathematics and its Applications, Vol. 33 (1991), Springer: Springer New York), 201-220 · Zbl 0735.62035 [19] Peracchi, F., Robust M-estimators, Economectric Reviews, 9, 1-30 (1990) [20] Rousseeuw, P. J.; Leroy, A., Robust regression and outliers detection (1987), Wiley: Wiley New York [21] Ruppert, D., On the bounded-influence regression estimator of Kransker and Welsch, Journal of the American Statistical Association, 80, 205-208 (1985) [22] Theil, H., Principles of econometrics (1971), North-Holland: North-Holland Amsterdam · Zbl 0221.62002 [23] Zellner, A., Statistical Theory and Econometrics, (Griliches, Z.; Intriligator, M. D., Handbook of econometrics, Vol. 1 (1983), North-Holland: North-Holland Amsterdam), Ch. 2 · Zbl 0545.62076
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