B1508
Title: Significance of explanatory variables when model is estimated by S-weighted estimator
Authors: Jan Amos Visek - Charles University in Prague (Czech Republic) [presenting]
Abstract: The S-weighted estimator is a generalization of the Least Weighted Squares as well as of S-estimator. It inherited all pros and removed restriction of LWS on the quadratic function. It depressed a potential high sensitivity to inliers and restriction on bounded objective function of S-estimator. The estimator is the argument which minimizes the scale of residuals under a constraint on the sum of products of weights and of order statistics of the squared residuals plugged into the objective function. So, it reaches a high flexibility of estimator and it can be tailored to the character and level of contamination of data. The consistency of new estimator was proved and the reliability of algorithm was demonstrated. Significance of the individual explanatory variable is a key diagnostic tool. It is surprising that there are nearly no results on this topics for the robust identification of model. Presumably it is due to the fact that - even if we start with i.i.d. framework - robustification transforms this framework to the framework with heteroscedasticity. The denominator of $t$-statistics is so the sum of independent random variables, each of them is the square of normal r.v.- but the r.v.'s have different variances. We obtain something like generalized chi-square-distribution and consequently generalized $t$-distribution. The distribution of generalized $t$-statistic has to be simulated.
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