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Paper shows that, under assumption that the single forecasts which enter the combination are unbiased, imposing some constraints on coordinates of <em>M </em>-estimator (of corresponding regression coefficients) leads to a gain in the asymptotic variance of one-step forward prediction evaluated by means...

The famous Durbin-Watson statistic is studied for the residuals from the least trimmed squared regression analysis. Having proved asymptotic linearity of corresponding functional (namely sum of h smallest squared residuals), an asymptotic representation of the least trimmed squares estimator is...

The consistency and the asymptotic normality of the least weighted squares is proved and its asymptotic representation derived. Although the proof includes rather large amount of technicalities, it is not difficult to follow. The technique as follows from the analogy with the least trimmed...

An example of possible misIeading role of the basic charaeteristics of the c1assical LB regression analysis is given. Another example using high breakdown point estimators demonstrates that in the case of contaminated data various estimators may give considerably different estimates....

Paper recalls motivation for generalized method of moments (GMM) as well as the idea estimated generalized method of moments. Having demonstrated the danger of underrating the heteroscedasticity of disturbances and recalling Cragg's idea of improvement of estimation under heteroscedasticity, it...

Consistency, asymptotic representation and asymptotic normality of the least trimmed squares estimator of regression coefficients is derived in the framework with random carriers. Also a result describing sensitivity to the deletion of an observation is given.

The consistency and the asymptotic normality of the least weighted squares is proved and its asymptotic representation derived. Although the proof includes rather large amount of technicalities, it is not difficult to follow. The technique as follows from the analogy with the least trimmed...

Several problems emerging with the studentization of M-estimators of regression model are briefly discussed and reasons for an enlargement of famous Hampel's program are given. Paper then presents a proposal of a scale-equivariant and regression-invariant scale estimator with an acceptable...

The effects of over- and underfitting the regression model is studied for M-estimators. Applying nowadays already classic tool, namely the asymptotic linearity of M-statistics, the Bahadur representation of M-estimators in over- and underfitted model is found. It allows to establish conditions...