Abstract
Consistency of the least weighted squares with constraints under heteroscedasticity 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 least trimmed squares). 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 empirical mean square errors and empirical variances} are reported.