| Title:
|
A note on asymptotic linearity of $M$-statistics in nonlinear models (English) |
| Author:
|
Rubio, Asunción Mária |
| Author:
|
Víšek, Jan Ámos |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
32 |
| Issue:
|
4 |
| Year:
|
1996 |
| Pages:
|
353-374 |
| . |
| Category:
|
math |
| . |
| MSC:
|
62F10 |
| MSC:
|
62F12 |
| MSC:
|
62J02 |
| idZBL:
|
Zbl 0882.62053 |
| idMR:
|
MR1420128 |
| . |
| Date available:
|
2009-09-24T19:03:29Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/124729 |
| . |
| Reference:
|
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| Reference:
|
[2] P. J. Bickel, M. J. Wichura: Convergence criteria for multiparameter stochastic processes and some applications.Ann. Math. Statist. 42 (1971), 1656-1670. Zbl 0265.60011, MR 0383482 |
| Reference:
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[3] M. Csörgö, P. Révész: Strong Approximation in Probability and Statistics.Akademia Kiadó, Budapest 1981. MR 0666546 |
| Reference:
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[4] P. L. Davis: Aspects of robust linear regression.Ann. Statist. 21 (1993), 1843-1899. MR 1245772 |
| Reference:
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| Reference:
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| Reference:
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[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 0990395 |
| Reference:
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[8] J. Jurečková, B. Procházka: Regression quantiles and trimmed least squares estimator in nonlinear regression model.Nonparametric Statist. 3 (1994), 201-222. MR 1291545 |
| Reference:
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[9] J. Jurečková, P. K. Sen: Uniform second order asymptotic linearity of $M$-statistics in linear models.Statist. Decisions 7 (1989), 263-276. MR 1029480 |
| Reference:
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[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 1089470 |
| Reference:
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[11] F. Liese, I. Vajda: Consistency of $M$-estimators in general models.J. Multivariate Anal. 50 (1994), 93-114. MR 1292610 |
| Reference:
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[12] A. Marazzi: Algorithms, Routines and S Functions for Robust Statistics.Wadsworth \& Brooks/Cole Advanced Books \& Software, Pacific Grove, California 1992. MR 1184396 |
| Reference:
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[13] J. M. Ortega, W. C. Rheinboldt: Iterative Solution of Nonlinear Equations in Several Variables.Academic Press, New York and London 1970. Zbl 0241.65046, MR 0273810 |
| Reference:
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[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 0786311 |
| Reference:
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[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 1172294 |
| Reference:
|
[16] A. Rubio L. Aguilar, J. Á. Víšek: Testing for difference between models.Comput. Statist. 8 (1992), 57-70. MR 1220337 |
| Reference:
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[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 1321760 |
| Reference:
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[18] J. Á. Víšek: Stability of regression models estimates with respect to subsamples.Computat. Statist. 7 (1992), 183-203. MR 1178353 |
| Reference:
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[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. |
| Reference:
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[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 1321759 |
| Reference:
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[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. |
| Reference:
|
[22] J. Á. Víšek: Sensitivity analysis of $M$-estimates.Ann. Inst. Statist. Math., to appear. MR 1424776 |
| . |
