<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>

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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...