Jan Ámos Víšek (2011)
Kybernetika
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A robust version of the Ordinary Least Squares accommodating the idea of weighting the order statistics of the squared residuals (rather than directly the squares of residuals) is recalled and its properties are studied. The existence of solution of the corresponding extremal problem and the consistency under heteroscedasticity is proved.
Jan Kalina (2011)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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Highly robust statistical and econometric methods have been developed not only as a diagnostic tool for standard methods, but they can be also used as self-standing methods for valid inference. Therefore the robust methods need to be equipped by their own diagnostic tools. This paper describes diagnostics for robust estimation of parameters in two econometric models derived from the linear regression. Both methods are special cases of the generalized method of moments estimator based...
TomĂĄĹĄ Jurczyk (2011)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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From the practical point of view the regression analysis and its Least Squares method is clearly one of the most used techniques of statistics. Unfortunately, if there is some problem present in the data (for example contamination), classical methods are not longer suitable. A lot of methods have been proposed to overcome these problematic situations. In this contribution we focus on special kind of methods based on trimming. There exist several approaches which use trimming off part...
Tadeusz Bednarski, Brenton R. Clarke, Daniel Schubert (2010)
Discussiones Mathematicae Probability and Statistics
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In this paper we derive an asymptotic normality result for an adaptive trimmed likelihood estimator of regression starting from initial high breakdownpoint robust regression estimates. The approach leads to quickly and easily computed robust and efficient estimates for regression. A highlight of the method is that it tends automatically in one algorithm to expose the outliers and give least squares estimates with the outliers removed. The idea is to begin with a rapidly computed consistent...
Jan Ámos Víšek (2011)
Acta Universitatis Carolinae. Mathematica et Physica
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Pavel Čížek (2008)
Applications of Mathematics
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The paper studies a new class of robust regression estimators based on the two-step least weighted squares (2S-LWS) estimator which employs data-adaptive weights determined from the empirical distribution or quantile functions of regression residuals obtained from an initial robust fit. Just like many existing two-step robust methods, the proposed 2S-LWS estimator preserves robust properties of the initial robust estimate. However, contrary to the existing methods, the first-order asymptotic...