Optimality of the least weighted squares estimator

Libor Mašíček

Kybernetika (2004)

  • Volume: 40, Issue: 6, page [715]-734
  • ISSN: 0023-5954

Abstract

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The present paper deals with least weighted squares estimator which is a robust estimator and it generalizes classical least trimmed squares. We will prove n -consistency and asymptotic normality for any sequence of roots of normal equation for location model. The influence function for general case is calculated. Finally optimality of this estimator is discussed and formula for most B-robust and most V-robust weights is derived.

How to cite

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Mašíček, Libor. "Optimality of the least weighted squares estimator." Kybernetika 40.6 (2004): [715]-734. <http://eudml.org/doc/33731>.

@article{Mašíček2004,
abstract = {The present paper deals with least weighted squares estimator which is a robust estimator and it generalizes classical least trimmed squares. We will prove $\sqrt\{n\}$-consistency and asymptotic normality for any sequence of roots of normal equation for location model. The influence function for general case is calculated. Finally optimality of this estimator is discussed and formula for most B-robust and most V-robust weights is derived.},
author = {Mašíček, Libor},
journal = {Kybernetika},
keywords = {robust regression; least trimmed squares; least weighted squares; influence function; $\sqrt\{n\}$-consistency; asymptotic normality; B-robustness; V-robustness; robust regression; least trimmed squares; -consistency; B-robustness; V-robustness},
language = {eng},
number = {6},
pages = {[715]-734},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Optimality of the least weighted squares estimator},
url = {http://eudml.org/doc/33731},
volume = {40},
year = {2004},
}

TY - JOUR
AU - Mašíček, Libor
TI - Optimality of the least weighted squares estimator
JO - Kybernetika
PY - 2004
PB - Institute of Information Theory and Automation AS CR
VL - 40
IS - 6
SP - [715]
EP - 734
AB - The present paper deals with least weighted squares estimator which is a robust estimator and it generalizes classical least trimmed squares. We will prove $\sqrt{n}$-consistency and asymptotic normality for any sequence of roots of normal equation for location model. The influence function for general case is calculated. Finally optimality of this estimator is discussed and formula for most B-robust and most V-robust weights is derived.
LA - eng
KW - robust regression; least trimmed squares; least weighted squares; influence function; $\sqrt{n}$-consistency; asymptotic normality; B-robustness; V-robustness; robust regression; least trimmed squares; -consistency; B-robustness; V-robustness
UR - http://eudml.org/doc/33731
ER -

References

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  1. Hampel F. R., Ronchetti E. M., Rousseeuw R. J., Stahel W. A., Robust Statistics – The Approach Based on Influence Function, Wiley, New York 1986 MR0829458
  2. Jurečková J., Asymptotic Representation of M-estimators of Location, Math. Operationsforsch. Statist., Ser. Statistics 11 (1980), 1, 61–73 (1980) Zbl0441.62037MR0606159
  3. Jurečková J., Sen P. K., Robust Statistical Procedures, Wiley, New York 1996 Zbl0862.62032MR1387346
  4. Mašíček L., Konzistence odhadu LWS pro parametr polohy (Consistency of LWS estimator for location model), KPMS Preprint 25, Department of Probability and Mathematical Statistics, Faculty of Mathemetics and Physics, Charles University, Prague 2002 
  5. Mašíček L., Konzistence odhadu LWS pro parametr polohy (Consistency of LWS estimator for location model), In: ROBUST’2002 (J. Antoch, G. Dohnal, and J. Klaschka, eds.), JČMF 2002, pp. 240–246 
  6. Rousseeuw P. J., Leroy A. M., Robust Regression and Outlier Detection, J.Wiley, New York 1987 Zbl0711.62030MR0914792
  7. Víšek J. Á., Regression with high breakdown point, In: ROBUST’2000 (J. Antoch and G. Dohnal, eds.), JČMF 2001, pp. 324–356 
  8. Víšek J. Á., A new paradigm of point estimation, In: Data Analysis 2000 – Modern Statistical Methods – Modelling, Regression, Classification and Data Mining (K. Kupka, ed.), TRILOBYTE Software 2001, pp. 195–230 

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