Geodesic
Optimality of the least weighted squares estimator
Kybernetika, Tome 40 (2004) no. 6, pp. 715-734 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $\sqrt{n}$-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.
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.
Classification : 62F10, 62F12, 62F35, 62J05
Keywords: robust regression; least trimmed squares; least weighted squares; influence function; $\sqrt{n}$-consistency; asymptotic normality; B-robustness; V-robustness 
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     author = {Ma\v{s}{\'\i}\v{c}ek, Libor},
     title = {Optimality of the least weighted squares estimator},
     journal = {Kybernetika},
     pages = {715--734},
     year = {2004},
     volume = {40},
     number = {6},
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     zbl = {1245.62013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2004_40_6_a5/}
}
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Mašíček, Libor. Optimality of the least weighted squares estimator. Kybernetika, Tome 40 (2004) no. 6, pp. 715-734. http://geodesic.mathdoc.fr/item/KYB_2004_40_6_a5/

[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 | MR

[2] Jurečková J.: Asymptotic Representation of M-estimators of Location. Math. Operationsforsch. Statist., Ser. Statistics 11 (1980), 1, 61–73 | MR | Zbl

[3] Jurečková J., Sen P. K.: Robust Statistical Procedures. Wiley, New York 1996 | MR | Zbl

[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 | MR | Zbl

[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