Selection Of Robust Method: Numerical Examples And Results

Examples of real data for which various robust methods give rather different estimates of regression model are presented and the reasons of the phenomenon are outlined. Two examples of invented data which enlighten for which kind of data we may expect the diversity of estimates (yielded even - or especially - by the estimators with high breakdown point) are also given. A formal reflection of the diversity of the estimates is offered. Results concerning the influence of deviations of the actual contamination level from the assumed one on the size (and power) of robust test is demonstrated for six (frequently used) probability distributions. Ideas how to cope with the situation are explored. Estimation of contamination level, size and power dependency, asymptotic linearity of M-statistics, subsample stability, residual homogeneity, test of significance of differences of the estimates and uniformity of consistency of M-estimators (of one type) are then recalled and discussed.