A note on asymptotic linearity of -statistics in nonlinear models
Asunción Rubio; Jan Ámos Víšek
Kybernetika (1996)
- Volume: 32, Issue: 4, page 353-374
- ISSN: 0023-5954
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topRubio, Asunción, and Víšek, Jan Ámos. "A note on asymptotic linearity of $M$-statistics in nonlinear models." Kybernetika 32.4 (1996): 353-374. <http://eudml.org/doc/27884>.
@article{Rubio1996,
author = {Rubio, Asunción, Víšek, Jan Ámos},
journal = {Kybernetika},
keywords = {rescaling of residuals; absolute continuity; -estimation; asymptotic linearity},
language = {eng},
number = {4},
pages = {353-374},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A note on asymptotic linearity of $M$-statistics in nonlinear models},
url = {http://eudml.org/doc/27884},
volume = {32},
year = {1996},
}
TY - JOUR
AU - Rubio, Asunción
AU - Víšek, Jan Ámos
TI - A note on asymptotic linearity of $M$-statistics in nonlinear models
JO - Kybernetika
PY - 1996
PB - Institute of Information Theory and Automation AS CR
VL - 32
IS - 4
SP - 353
EP - 374
LA - eng
KW - rescaling of residuals; absolute continuity; -estimation; asymptotic linearity
UR - http://eudml.org/doc/27884
ER -
References
top- D. M. Bates, D. G. Watts, Nonlinear Regression Analysis and Its Applications, J. Wiley & Sons, New York 1988. (1988) Zbl0728.62062MR1060528
- P. J. Bickel, M. J. Wichura, Convergence criteria for multiparameter stochastic processes and some applications, Ann. Math. Statist. 42 (1971), 1656-1670. (1971) Zbl0265.60011MR0383482
- M. Csörgö, P. Révész, Strong Approximation in Probability and Statistics, Akademia Kiadó, Budapest 1981. (1981) MR0666546
- P. L. Davis, Aspects of robust linear regression, Ann. Statist. 21 (1993), 1843-1899. (1993) MR1245772
- 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. (1986) MR0829458
- P. J. Huber, Robust estimation of a location parameter, Ann. Math. Statist. 35 (1964), 73-101. (1964) Zbl0136.39805MR0161415
- J. Jurečková, Consistency of -estimators in linear model generated by non-monotone and discontinuous -functions, Probab. Math. Statist. 10 (1988), 1-10. (1988) MR0990395
- J. Jurečková, B. Procházka, Regression quantiles and trimmed least squares estimator in nonlinear regression model, Nonparametric Statist. 3 (1994), 201-222. (1994) MR1291545
- J. Jurečková, P. K. Sen, Uniform second order asymptotic linearity of -statistics in linear models, Statist. Decisions 7 (1989), 263-276. (1989) MR1029480
- J. Jurečková, A. H. Welsh, Asymptotic relations between - and -estimators in the linear model, Ann. Inst. Statist. Math. 42 (1990), 671-698. (1990) MR1089470
- F. Liese, I. Vajda, Consistency of -estimators in general models, J. Multivariate Anal. 50 (1994), 93-114. (1994) MR1292610
- A. Marazzi, Algorithms, Routines and S Functions for Robust Statistics, Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, California 1992. (1992) MR1184396
- J. M. Ortega, W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York and London 1970. (1970) Zbl0241.65046MR0273810
- 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. (1983) MR0786311
- C. R. Rao, L. C. Zhao, On the consistency of -estimate in linear model obtained through an estimating equation, Statist. Probab. Lett. 14 (1992), 79-84. (1992) MR1172294
- A. Rubio L. Aguilar, J. Á. Víšek, Testing for difference between models, Comput. Statist. 8 (1992), 57-70. (1992) MR1220337
- A. Rubio F. Quintana, J. Á. Víšek, Test for differences of -estimates between nonlinear regression models, Probab. Math. Statist. 14 (1993), 2, 189-206. (1993) MR1321760
- J. Á. Víšek, Stability of regression models estimates with respect to subsamples, Computat. Statist. 7 (1992), 183-203. (1992) MR1178353
- 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. (1992)
- 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. (1993) MR1321759
- 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. (1994)
- J. Á. Víšek, Sensitivity analysis of -estimates, Ann. Inst. Statist. Math., to appear. MR1424776
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