# Article

Full entry | PDF   (1.0 MB)
Keywords:
robust regression; the least trimmed squares; $\sqrt{n}$-consistency; asymptotic normality
Summary:
$\sqrt{n}$-consistency of the least trimmed squares estimator is proved under general conditions. The proof is based on deriving the asymptotic linearity of normal equations.
References:
[1] Čížek P.: Analýza citlivosti $k$-krokových $M$-odhadů (Sensitivity analysis of $k$-step $M$-estimators, in Czech). Diploma Thesis, Czech Technical University, Prague 1996
[2] Hewitt E., Stromberg K.: Real and Abstract Analysis. Springer–Verlag, Berlin 1965 MR 0367121 | Zbl 0307.28001
[3] Víšek J. Á.: Sensitivity analysis $M$-estimates. Ann. Inst. Statist. Math. 48 (1996), 469–495 DOI 10.1007/BF00050849 | MR 1424776
[4] Víšek J. Á.: The least trimmed squares. Part I. Consistency. Kybernetika 42 (2006), 1–36 MR 2208518
[5] Víšek J. Á.: Kolmogorov–Smirnov statistics in linear regression. In: Proc. ROBUST 2006, submitted

Partner of