Publication detail

Víšek, J. Á.: Representation of the least weighted squares

Author(s): prof. RNDr. Jan Ámos Víšek CSc.,
Type: Articles in journals with impact factor
Year: 2015
Number: 47
ISSN / ISBN:
Published in: Advances and Applications in Statistics 47, 2015, 91 - 144.
Publishing place:
Keywords: Robust estimation of regression model, weighting the order statistics of squared residuals, Bahadur representation of the least weighted squares
JEL codes:
Suggested Citation:
Grants: GAČR 13-01930S Robust methods for nonstandard situations, their diagnostics and implementations
Abstract: The estimation of the coefficients of linear regression model by means of the Least Weighted Squares 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 Visek2000, 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. The consistency and root-consistency was studied in previous papers. So that present paper concludes the study of the basic properties of the estimator offering a derivation of asymptotic representation of the estimator.

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