Advances and Applications in Statistics
Volume 47, Issue 2, Pages 91 - 144
(November 2015) http://dx.doi.org/10.17654/ADASNov2015_091_144 |
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REPRESENTATION OF THE LEAST WEIGHTED SQUARES
Jan Ãmos VÃÅ¡ek
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Abstract: The estimation of the coefficients of linear regression model by means of the least weighted squares (LWS) is studied. The order of words in the name of method - the least weighted squares - is to hint that the weights are assigned to the order statistics of squared residuals rather than directly to the residuals. Although the proposal of the least weighted squares appeared already in Víšek [26], we have not yet any sufficiently general proof of their properties. However, new results about the uniform convergence of the empirical distribution functions in the regression framework opened the way, see Víšek [31] and [37]. The consistency and -consistency were studied in Víšek [36] and [35], respectively (see also Víšek [38]). So that present paper concludes the study of the basic properties of the estimator offering a derivation of asymptotic representation of the estimator. |
Keywords and phrases: robustness, implicit weighting, consistency of estimate by the least weighted squares. |
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