The behavior of the robust version of the classical  instrumental variables, called instrumental weighted variables, and  their asymptotic representation is studied by means of the Monte Carlo experiments under various frameworks. The results are given both in the !compressed'' form of...

It is straightforward that breaking the <em>orthogonalitycondition</em> implies biased and inconsistent estimates by means of the<em> ordinary least squares</em>. If moreover, the data are contaminatedit may significantly worsen the data processing, even if it is performed by <em> instrumental variables</em> or the ...</em>

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...

The result of Clemen (1986) shows that the combination of unbiased forecasts by means of a LS-regression model without an intercept and with the constraint that coefficients sum to one gives less spread prediction than the general regression model. Here the result is generalized for the M...

Examples of real data for which various robust methods give rather different estimates of regression model are presented and the reasons of the phenomenon are outlined. Two examples of invented data which enlighten for which kind of data we may expect the diversity of estimates (yielded even -...

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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....