Fast and robust bootstrap in seemingly unrelated regression models

Seemingly unrelated regression models generalize ordinary linear regression models by considering multiple regression equations that are linked by contemporaneously correlated disturbances. Traditional estimators allow this feature of correlated error terms, but they are extremely vulnerable to the presence of contamination in the data. Therefore, robust estimators for seemingly unrelated regression models are considered. S-estimators can attain a high breakdown point, but their normal efficiency can be quite low. For that reason, MM-estimators are introduced to obtain estimators that have both a high breakdown point and a high normal efficiency. Furthermore, the problem of statistical inference is studied. Asymptotic inference relies on assumptions which are hard to verify. Moreover, this inference may be non-robust. Bootstrapping on the other hand, requires less strict assumptions but lacks speed and robustness. Therefore, a fast and robust bootstrap procedure is developed. Robust bootstrap condence intervals of the unknown parameters in seemingly unrelated regression models are constructed and their performance is analyzed in simulation studies. In addition, hypothesis tests regarding the regression coefficients are carried out by bootstrapping a robust version of the likelihood-ratio statistic. The robust estimators and the fast and robust bootstrap procedure are illustrated on real data.status: publishe