A note on asymptotic linearity of $M$-statistics in nonlinear models
Kybernetika, Tome 32 (1996) no. 4, pp. 353-374
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Classification : 62F10, 62F12, 62J02
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     title = {A note on asymptotic linearity of $M$-statistics in nonlinear models},
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Rubio, Asunción Mária; Víšek, Jan Ámos. A note on asymptotic linearity of $M$-statistics in nonlinear models. Kybernetika, Tome 32 (1996) no. 4, pp. 353-374. http://geodesic.mathdoc.fr/item/KYB_1996_32_4_a2/

[1] D. M. Bates, D. G. Watts: Nonlinear Regression Analysis and Its Applications. J. Wiley \& Sons, New York 1988. | MR | Zbl

[2] P. J. Bickel, M. J. Wichura: Convergence criteria for multiparameter stochastic processes and some applications. Ann. Math. Statist. 42 (1971), 1656-1670. | MR | Zbl

[3] M. Csörgö, P. Révész: Strong Approximation in Probability and Statistics. Akademia Kiadó, Budapest 1981. | MR

[4] P. L. Davis: Aspects of robust linear regression. Ann. Statist. 21 (1993), 1843-1899. | MR

[5] F. R. Hampel E. M. Ronchetti P. J. Rousseeuw, W. A. Stahel: Robust Statistics -- The Approach Based on Influence Functions. J. Wiley \& Sons, New York 1986. | MR

[6] P. J. Huber: Robust estimation of a location parameter. Ann. Math. Statist. 35 (1964), 73-101. | MR | Zbl

[7] J. Jurečková: Consistency of $M$-estimators in linear model generated by non-monotone and discontinuous $\psi$-functions. Probab. Math. Statist. 10 (1988), 1-10. | MR

[8] J. Jurečková, B. Procházka: Regression quantiles and trimmed least squares estimator in nonlinear regression model. Nonparametric Statist. 3 (1994), 201-222. | MR

[9] J. Jurečková, P. K. Sen: Uniform second order asymptotic linearity of $M$-statistics in linear models. Statist. Decisions 7 (1989), 263-276. | MR

[10] J. Jurečková, A. H. Welsh: Asymptotic relations between $L$- and $M$-estimators in the linear model. Ann. Inst. Statist. Math. 42 (1990), 671-698. | MR

[11] F. Liese, I. Vajda: Consistency of $M$-estimators in general models. J. Multivariate Anal. 50 (1994), 93-114. | MR

[12] A. Marazzi: Algorithms, Routines and S Functions for Robust Statistics. Wadsworth \& Brooks/Cole Advanced Books \& Software, Pacific Grove, California 1992. | MR

[13] J. M. Ortega, W. C. Rheinboldt: Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York and London 1970. | MR | Zbl

[14] S. Portnoy: Tightness of the sequence of empiric c.d.f. processes defined from regression fractiles. In: Robust and Nonlinear Time-Series Analysis (J. Franke, W. Hardle, D. Martin, eds.), Springer-Verlag, New York, 1983, pp. 231-246. | MR

[15] C. R. Rao, L. C. Zhao: On the consistency of $M$-estimate in linear model obtained through an estimating equation. Statist. Probab. Lett. 14 (1992), 79-84. | MR

[16] A. Rubio L. Aguilar, J. Á. Víšek: Testing for difference between models. Comput. Statist. 8 (1992), 57-70. | MR

[17] A. Rubio F. Quintana, J. Á. Víšek: Test for differences of $M$-estimates between nonlinear regression models. Probab. Math. Statist. 14 (1993), 2, 189-206. | MR

[18] J. Á. Víšek: Stability of regression models estimates with respect to subsamples. Computat. Statist. 7 (1992), 183-203. | MR

[19] J. Á. Víšek: Problems connected with selection of robust procedure. In: Proceedings of PROBASTAT'91 (A. Pázman and J. Volaufová, eds.), Printing House of the Technical University of Liptovský Mikuláš 1992, pp. 189-203.

[20] J. Á. Víšek: On the role of contamination level and the least favorable behaviour of gross-error sensitivity. Probab. Math. Statist. 14 (1993), 2, 173-187. | MR

[21] J. Á. Víšek: A cautionary note on the method of Least Median of Squares reconsidered. In: Transactions of the Twelfth Prague Conference on Information Theory, Statistical Decision Functions and Random Processes (J. Á. Víšek and P. Lachout, eds.), Prague 1994, pp. 254-259.

[22] J. Á. Víšek: Sensitivity analysis of $M$-estimates. Ann. Inst. Statist. Math., to appear. | MR