Influences of classification on linear regression estimations (Q2763279)

The influence of data classification (creation of classes) on the estimation of regression parameters (normal regression) is studied. Various rules for the determination of the number of results belonging to classes are discussed. Systematic and random errors in the estimation of parameters occur. A model of mixture distributions for groued data, if the values of regressors are classified, is used. The mixture distributions are created by conditional distributions, which describe the influence of a classification. The modified regression estimates are not BLU and consistent, but they are asymptotic BLU and consistent, if the lengths of classes converge to zero.NEWLINENEWLINENEWLINEThe results of the theoretical part are numerically verified on simulated data. The reagibility of regression estimaties is here in focus. The sample distributions are approximated using Monte-Carlo simulations. The connected computational programs are also published. The procedures based on classifications can be applied to family budget data or to secondary statistical resources.