The least weighted squares with constraints and under heteroscedasticity
<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 making idea about the spread of the estimator is briefly discussed in the framework of numerical study. The pros and cons of the estimator are also summarized. The loss of efficiency of the estimator, when there is no contamination, as well as an increase of variance caused by collinearity are also addressed. Behaviour of the estimator with constraints under various types and levels of contamination (when simultaneously the collinearity of design matrix and the heteroscedasticity of disturbances take place) is studied. The </span><span style="font-size: 11.000000pt; font-family: 'CMTI10';">empirical mean square errors </span><span style="font-size: 11.000000pt; font-family: 'CMR10';">and </span><span style="font-size: 11.000000pt; font-family: 'CMTI10';">empirical variances </span><span style="font-size: 11.000000pt; font-family: 'CMR10';">are reported. </span><p>
