The least trimmed squares. Part III: Asymptotic normality
Kybernetika (2006)
- Volume: 42, Issue: 2, page 203-224
- ISSN: 0023-5954
Access Full Article
topAbstract
topHow to cite
topVíšek, Jan Ámos. "The least trimmed squares. Part III: Asymptotic normality." Kybernetika 42.2 (2006): 203-224. <http://eudml.org/doc/33801>.
@article{Víšek2006,
abstract = {Asymptotic normality of the least trimmed squares estimator is proved under general conditions. At the end of paper a discussion of applicability of the estimator (including the discussion of algorithm for its evaluation) is offered.},
author = {Víšek, Jan Ámos},
journal = {Kybernetika},
keywords = {robust regression; the least trimmed squares; $\sqrt\{n\}$-consistency; asymptotic normality; robust regression; -consistency},
language = {eng},
number = {2},
pages = {203-224},
publisher = {Institute of Information Theory and Automation AS CR},
title = {The least trimmed squares. Part III: Asymptotic normality},
url = {http://eudml.org/doc/33801},
volume = {42},
year = {2006},
}
TY - JOUR
AU - Víšek, Jan Ámos
TI - The least trimmed squares. Part III: Asymptotic normality
JO - Kybernetika
PY - 2006
PB - Institute of Information Theory and Automation AS CR
VL - 42
IS - 2
SP - 203
EP - 224
AB - Asymptotic normality of the least trimmed squares estimator is proved under general conditions. At the end of paper a discussion of applicability of the estimator (including the discussion of algorithm for its evaluation) is offered.
LA - eng
KW - robust regression; the least trimmed squares; $\sqrt{n}$-consistency; asymptotic normality; robust regression; -consistency
UR - http://eudml.org/doc/33801
ER -
References
top- Benáček V. J., Jarolím, M., Víšek J. Á., Supply-side characteristics and the industrial structure of Czech foreign trade, In: Proc. Business and Economic Development in Central and Eastern Erupe: Implications for Economic Integration into wider Europe. Technical University in Brno and University of Wisconsin, Whitewater, and the Nottingham Trent University 1998, pp. 51–68 (1998)
- Boček P., Lachout P., 10.1016/0167-9473(93)E0051-5, Comput. Statist. Data Anal. (Memorial volume) 19(1995), 129–134 (1995) Zbl0875.62292MR1323269DOI10.1016/0167-9473(93)E0051-5
- Breiman L., Probability, Addison–Wesley Publishing Company, London 1968 Zbl0753.60001MR0229267
- Chatterjee S., Hadi A. S., Sensitivity Analysis in Linear Regression, Wiley, New York 1988 Zbl0648.62066MR0939610
- Čížek P., Robust estimation with discrete explanatory variables, In: COMPSTAT 2003, pp. 509–514 MR1986578
- Čížek P., Víšek J. Á., Least trimmed squares, In: EXPLORE, Application Guide (W. Härdle, Z. Hlavka, and S. Klinke, eds.), Springer–Verlag, Berlin 2000, pp. 49–64
- Jurečková J., (1993) P. K. Sen, Regression rank scores scale statistics and studentization in linear models, In: Proc. Fifth Prague Symposium on Asymptotic Statistics, Physica–Verlag, Heidelberg 1993, pp. 111–121 (1993) MR1311932
- Hampel F. R., Ronchetti E. M., Rousseeuw P. J., Stahel W. A., Robust Statistics – The Approach Based on Influence Functions, Wiley, New York 1986 Zbl0733.62038MR0829458
- Hawkins D. M., Olive D. J., 10.1016/S0167-9473(98)00082-6, Comput. Statist. Data Anal. 30 (1999), 1, 1–12 (1999) MR1681450DOI10.1016/S0167-9473(98)00082-6
- Hettmansperger T. P., Sheather S. J., A cautionary note on the method of least median squares, Amer. Statist. 46 (1992), 79–83 (1992) MR1165565
- Huber P. J., Robust Statistics, Wiley, New York 1981 MR0606374
- Liese F., Vajda I., 10.1006/jmva.1994.1036, J. Multivar. Anal. 50 (1994), 93–114 (1994) MR1292610DOI10.1006/jmva.1994.1036
- Maronna R. A., Yohai V. J., 10.1007/BF00536192, Z. Wahrscheinlichkeitstheorie verw. Gebiete 58 (1981), 7–20 (1981) MR0635268DOI10.1007/BF00536192
- Pollard D., 10.1017/S0266466600004394, Econometric Theory 7 (1991), 186–199 (1991) MR1128411DOI10.1017/S0266466600004394
- Portnoy S., Tightness of the sequence of empiric c, d.f. processes defined from regression fractiles. In: Robust and Nonlinear Time-Series Analysis (J. Franke, W. Härdle, and D. Martin, eds.), Springer–Verlag, New York 1983, pp. 231–246 (1983) MR0786311
- Rousseeuw P. J., Leroy A. M., Robust Regression and Outlier Detection, Wiley, New York 1987 Zbl0711.62030MR0914792
- Rubio A. M., Víšek J. Á., Estimating the contamination level of data in the framework of linear regression analysis, Qűestiió 21 (1997), 9–36 (1997) Zbl1167.62388MR1476149
- Štěpán J., Teorie pravděpodobnosti (Probability Theory), Academia, Prague 1987
- Víšek J. Á., A cautionary note on the method of Least Median of Squares reconsidered, In: Trans. Twelfth Prague Conference on Inform. Theory, Statist. Dec. Functions and Random Processes, Prague 1994, pp. 254–259 (1994)
- Víšek J. Á., On high breakdown point estimation, Comput. Statistics 11 (1996), 137–146 (1996) Zbl0933.62015MR1394545
- Víšek J. Á., 10.1007/BF00050849, Ann. Inst. Statist. Math. 48 (1996), 469–495 (1996) MR1424776DOI10.1007/BF00050849
- Víšek J. Á., Diagnostics of regression subsample stability, Probab. Math. Statist. 17 (1997), 2, 231–257 (1997) Zbl0924.62072MR1490803
- Víšek J. Á., Robust estimation of regression model, Bull. Czech Econometric Society 9 (1999), 57–79 (1999)
- Víšek J. Á., The least trimmed squares – random carriers, Bull. Czech Econometric Society 10 (1999), 1–30 (1999)
- Víšek J. Á., The robust regression and the experiences from its application on estimation of parameters in a dual economy, In: Proc. Macromodels’99, Rydzyna 1999,pp. 424–445 (1999)
- Víšek J. Á., 10.1016/S0167-9473(99)00068-7, Comput. Statist. Data Anal. 34 (2000) 67–89 Zbl1052.62509DOI10.1016/S0167-9473(99)00068-7
- Víšek J. Á., Regression with high breakdown point, In: Robust 2000 (J. Antoch and G. Dohnal, eds.), Union of the Czechoslovak Mathematicians and Physicists, Prague 2001, 324–356
- Víšek J. Á., 10.1023/A:1022465701229, Ann. Inst. Statist. Math. 54 (2002), 2, 261–290 Zbl1013.62072MR1910173DOI10.1023/A:1022465701229
- Víšek J. Á., The least weighted squares I, The asymptotic linearity of normal equation. Bull. Czech Econometric Society 9 (2002), 15, 31–58
- Víšek J. Á., The least weighted squares II, Consistency and asymptotic normality. Bull. Czech Econometric Society 9 (2002), 16, 1–28
- Víšek J. Á., Kolmogorov–Smirnov statistics in linear regression, In: Proc. ROBUST 2006, submitted
- Víšek J. Á., Least trimmed squares – sensitivity study, In: Proc. Prague Stochastics 2006, submitted
- Zvára K., Regresní analýza (Regression Analysis – in Czech), Academia, Prague 1989
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.