The least trimmed squares. Part I: Consistency

Jan Ámos Víšek

Kybernetika (2006)

  • Volume: 42, Issue: 1, page 1-36
  • ISSN: 0023-5954

Abstract

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The consistency of the least trimmed squares estimator (see Rousseeuw [Rous] or Hampel et al. [HamRonRouSta]) is proved under general conditions. The assumptions employed in paper are discussed in details to clarify the consequences for the applications.

How to cite

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Víšek, Jan Ámos. "The least trimmed squares. Part I: Consistency." Kybernetika 42.1 (2006): 1-36. <http://eudml.org/doc/33790>.

@article{Víšek2006,
abstract = {The consistency of the least trimmed squares estimator (see Rousseeuw [Rous] or Hampel et al. [HamRonRouSta]) is proved under general conditions. The assumptions employed in paper are discussed in details to clarify the consequences for the applications.},
author = {Víšek, Jan Ámos},
journal = {Kybernetika},
keywords = {robust regression; the least trimmed squares; consistency; discussion of assumptions and of algorithm for evaluation of estimator; robust regression},
language = {eng},
number = {1},
pages = {1-36},
publisher = {Institute of Information Theory and Automation AS CR},
title = {The least trimmed squares. Part I: Consistency},
url = {http://eudml.org/doc/33790},
volume = {42},
year = {2006},
}

TY - JOUR
AU - Víšek, Jan Ámos
TI - The least trimmed squares. Part I: Consistency
JO - Kybernetika
PY - 2006
PB - Institute of Information Theory and Automation AS CR
VL - 42
IS - 1
SP - 1
EP - 36
AB - The consistency of the least trimmed squares estimator (see Rousseeuw [Rous] or Hampel et al. [HamRonRouSta]) is proved under general conditions. The assumptions employed in paper are discussed in details to clarify the consequences for the applications.
LA - eng
KW - robust regression; the least trimmed squares; consistency; discussion of assumptions and of algorithm for evaluation of estimator; robust regression
UR - http://eudml.org/doc/33790
ER -

References

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  1. Andrews D. W. K., 10.2307/1913568, Econometrica 55 (1987), 1465–1471 (1987) Zbl0646.62101MR0923471DOI10.2307/1913568
  2. Bickel P. J., 10.1080/01621459.1975.10479884, J. Amer. Statist. Assoc. 70 (1975), 428–433 (1975) Zbl0322.62038MR0386168DOI10.1080/01621459.1975.10479884
  3. Breiman L., Probability, Addison–Wesley, London 1968 Zbl0753.60001MR0229267
  4. Chatterjee S., Hadi A. S., Sensitivity Analysis in Linear Regression, Wiley, New York 1988 Zbl0648.62066MR0939610
  5. Csőrgő M., Révész P., Strong Approximation in Probability and Statistics, Akademia Kiadó, Budapest 1981 MR0666546
  6. Dhrymes P. J., Introductory Econometrics, Springer–Verlag, New York 1978 Zbl0388.62096MR0545505
  7. Jurečková J., Sen P. K., 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. Hettmansperger T. P., Sheather S. J., A cautionary note on the method of least median squares, Amer. Statist. 46 (1992), 79–83 (1992) MR1165565
  10. Liese F., Vajda I., 10.1006/jmva.1994.1036, J. Multivar. Anal. 50 (1994), 93–114 (1994) MR1292610DOI10.1006/jmva.1994.1036
  11. 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
  12. Prigogine I., Stengers I., La Nouvelle Alliance, SCIENTIA 1977, Issues 5–12 (1977) 
  13. Prigogine I., Stengers I., Out of Chaos, William Heinemann Ltd, London 1984 MR0102205
  14. Rousseeuw P. J., 10.1080/01621459.1984.10477105, J. Amer. Statist. Assoc. 79 (1984), 871–880 (1984) MR0770281DOI10.1080/01621459.1984.10477105
  15. Rousseeuw P. J., Leroy A. M., Robust Regression and Outlier Detection, Wiley, New York 1987 Zbl0711.62030MR0914792
  16. Rubio A. M., Víšek J. Á., A note on asymptotic linearity of M -statistics in nonlinear models, Kybernetika 32 (1996), 353–374 (1996) Zbl0882.62053MR1420128
  17. Rubio A. M., Víšek J. Á., Estimating the contamination level of data in the framework of linear regression analysis, Qüestiió 21 (1997), 9–36 (1997) Zbl1167.62388MR1476149
  18. Štěpán J., Teorie pravděpodobnosti (Probability Theory), Academia, Prague 1987 
  19. Huffel S. Van, Total least squares and error-in-variables modelling: Bridging the gap between statistics, computational mathematics and enginnering, In: Proc. Computational Statistics, COMPSTAT 2004 (J. Antoch, ed.), Physica–Verlag, Springer 2004, pp. 539–555 MR2173049
  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., Ekonometrie I (Econometrics I), Carolinum, Publishing House of Charles University, Prague 1997 
  23. Víšek J. Á., Robust specification test, In: Proc. Prague Stochastics’98 (M. Hušková, P. Lachout, and J. Á. Víšek, eds.), Union of Czechoslovak Mathematicians and Physicists, Prague 1998, pp. 581–586 (1998) 
  24. Víšek J. Á., Robust instruments, In: Robust’98 (J. Antoch and G. Dohnal, eds.), Union of Czechoslovak Mathematicians and Physicists, Prague 1998, pp. 195–224 (1998) 
  25. Víšek J. Á., Robust estimation of regression model, Bull. Czech Econometric Society 9 (1999), 57–79 (1999) 
  26. Víšek J. Á., The least trimmed squares – random carriers, Bull. Czech Econometric Society 10 (1999), 1–30 (1999) 
  27. 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) 
  28. 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
  29. Víšek J. Á., Regression with high breakdown point, In: Robust 2000 (J. Antoch and G. Dohnal, eds.), Union of Czechoslovak Mathematicians and Physicists, Prague 2001, pp. 324–356 
  30. Víšek J. Á., A new paradigm of point estimation, In: Proc. Data Analysis 2000/II, Modern Statistical Methods – Modelling, Regression, Classification and Data Mining (K. Kupka, ed.), TRYLOBITE, Pardubice 2000, 195–230 
  31. Víšek J. Á., 10.1023/A:1022465701229, Ann. Inst. Statist. Math. 54 (2002), 2, 261–290 Zbl1013.62072MR1910173DOI10.1023/A:1022465701229
  32. Víšek J. Á., n -consistency of empirical distribution function of residuals in linear regression model, Probab. Lett., submitted 
  33. Zvára K., Regresní analýza (Regression Analysis), Academia, Prague 1989 

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