The least trimmed squares. Part III: Asymptotic normality

Jan Ámos Víšek

Kybernetika (2006)

  • Volume: 42, Issue: 2, page 203-224
  • ISSN: 0023-5954

Abstract

top
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.

How to cite

top

Víšek, 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
  1. 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) 
  2. 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
  3. Breiman L., Probability, Addison–Wesley Publishing Company, London 1968 Zbl0753.60001MR0229267
  4. Chatterjee S., Hadi A. S., Sensitivity Analysis in Linear Regression, Wiley, New York 1988 Zbl0648.62066MR0939610
  5. Čížek P., Robust estimation with discrete explanatory variables, In: COMPSTAT 2003, pp. 509–514 MR1986578
  6. 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 
  7. 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
  8. 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
  9. 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
  10. Hettmansperger T. P., Sheather S. J., A cautionary note on the method of least median squares, Amer. Statist. 46 (1992), 79–83 (1992) MR1165565
  11. Huber P. J., Robust Statistics, Wiley, New York 1981 MR0606374
  12. Liese F., Vajda I., 10.1006/jmva.1994.1036, J. Multivar. Anal. 50 (1994), 93–114 (1994) MR1292610DOI10.1006/jmva.1994.1036
  13. Maronna R. A., Yohai V. J., 10.1007/BF00536192, Z. Wahrscheinlichkeitstheorie verw. Gebiete 58 (1981), 7–20 (1981) MR0635268DOI10.1007/BF00536192
  14. Pollard D., 10.1017/S0266466600004394, Econometric Theory 7 (1991), 186–199 (1991) MR1128411DOI10.1017/S0266466600004394
  15. 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
  16. Rousseeuw P. J., Leroy A. M., Robust Regression and Outlier Detection, Wiley, New York 1987 Zbl0711.62030MR0914792
  17. 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
  18. Štěpán J., Teorie pravděpodobnosti (Probability Theory), Academia, Prague 1987 
  19. 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) 
  20. Víšek J. Á., On high breakdown point estimation, Comput. Statistics 11 (1996), 137–146 (1996) Zbl0933.62015MR1394545
  21. Víšek J. Á., 10.1007/BF00050849, Ann. Inst. Statist. Math. 48 (1996), 469–495 (1996) MR1424776DOI10.1007/BF00050849
  22. Víšek J. Á., Diagnostics of regression subsample stability, Probab. Math. Statist. 17 (1997), 2, 231–257 (1997) Zbl0924.62072MR1490803
  23. Víšek J. Á., Robust estimation of regression model, Bull. Czech Econometric Society 9 (1999), 57–79 (1999) 
  24. Víšek J. Á., The least trimmed squares – random carriers, Bull. Czech Econometric Society 10 (1999), 1–30 (1999) 
  25. 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) 
  26. 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
  27. 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 
  28. Víšek J. Á., 10.1023/A:1022465701229, Ann. Inst. Statist. Math. 54 (2002), 2, 261–290 Zbl1013.62072MR1910173DOI10.1023/A:1022465701229
  29. Víšek J. Á., The least weighted squares I, The asymptotic linearity of normal equation. Bull. Czech Econometric Society 9 (2002), 15, 31–58 
  30. Víšek J. Á., The least weighted squares II, Consistency and asymptotic normality. Bull. Czech Econometric Society 9 (2002), 16, 1–28 
  31. Víšek J. Á., Kolmogorov–Smirnov statistics in linear regression, In: Proc. ROBUST 2006, submitted 
  32. Víšek J. Á., Least trimmed squares – sensitivity study, In: Proc. Prague Stochastics 2006, submitted 
  33. Zvára K., Regresní analýza (Regression Analysis – in Czech), Academia, Prague 1989 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.