Joint Research Conference

June 24-26, 2014

Test of Nested Robustly Estimated Models

Abstract:

The test of a restricted verses an unrestricted model is a basic and very important task in regression analysis (similarly as the evaluation of significance of a given explanatory variable). The classical solution of the problem is crucially based on the orthogonality of the corresponding residual sums of squares. Orthogonality then, due to the assumed normality of disturbances, implies the independence of the sums in question and consequently (properly standardized) ratio of these sums has the Fisher-Snedecor d. f. This task is not yet addressed for any robust estimator of a regression model. The reason is that the most of robust estimators are defined in a such way that the L2-metric of the Euclidean space is distorted and the orthogonality of the residual sums of squares is lost. We will study this task for the least weighted squares (LWS) which is the estimator defined as a slightly modified ordinary least squares estimator (OLS). LWS however, in contrast to the OLS, is not vulnerable to the contamination of data and it doesn't suffer the effect as the least median of squares or the least trimmed squares. The basic trick to find some results (especially the existence of the solution of the extreme problem which defines LWS) for the least weighted squares is possibility to show the equivalence of LWS with the classical weighted least squares applied on properly permuted data.