Asymptotic properties of the weighted least squares estimate

This diploma thesis dissertate about consistency and asymptotic representation of the least weighted squares estimator (LWS). In preface we mention reasons for data processing with robust statistical methods and differencies between LWS estimator and other methods (the least squares estimator, the least trimmed squares estimator). In the following sections we show proofs of lemmas about consistency and assymptotic representation of the least weighted squares estimator. Compared to the similar results published before we have concluded ours based on different conditions. Impulse for this thesis were new results about uniform convergence of empirical function mentioned in work from prof. Jan Ámos Víšek - Kolmogorov-Smirnov statistics in multiple regression from year 2006 (see Víšek (2006a))