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...

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 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...

<p>The  robust version of the classical  instrumental variables, called Instrumental Weighted Variables (IWV) and the conditions for its consistency and $\sqrt{n}$-consistency  are recalled. The reasons  why the classical instrumental variables as well as  IWV were introduced and the idea of...</p>

  <p><span style="font-size: 11.000000pt; font-family: 'CMTI10';">Consistency </span><span style="font-size: 11.000000pt; font-family: 'CMR10';">of the </span><span style="font-size: 11.000000pt; font-family: 'CMTI10';">least weighted squares with constraints </span><span style="font-size: 11.000000pt; font-family: 'CMR10';">under </span><span style="font-size: 11.000000pt; font-family: 'CMTI10';">heteroscedasticity </span><span style="font-size: 11.000000pt; font-family: 'CMR10';">is proved and the patterns of numerical study (for the whole collection of situations) reveals its finite sample properties (on the background of the well-known </span><span style="font-size: 11.000000pt; font-family: 'CMTI10';">least trimmed squares</span><span style="font-size: 11.000000pt; font-family: 'CMR10';">). The possibility of...</span></p>