Geodesic
Optimality of the least weighted squares estimator
Kybernetika, Tome 40 (2004) no. 6, p. [715]

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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.
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 
@article{KYB_2004__40_6_a5,
     author = {Ma\v{s}{\'\i}\v{c}ek, Libor},
     title = {Optimality of the least weighted squares estimator},
     journal = {Kybernetika},
     pages = {[715]},
     publisher = {mathdoc},
     volume = {40},
     number = {6},
     year = {2004},
     mrnumber = {2120393},
     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, p. [715]. http://geodesic.mathdoc.fr/item/KYB_2004__40_6_a5/