Improving the efficiency and efficacy of robust sequential bifurcation under data contamination

Abstract

Robust sequential bifurcation (RSB) is an outlier-resistant factor screening method. It combines robust statistics with the sequential bifurcation procedure, which can handle the factor screening problem when response data is contaminated. Due to the low relative efficiency of robust estimator (median & MAD) and apparent discrepancy between the robust statistic and standard normal distribution, RSB is further improved on efficiency and efficacy in this article. Firstly, the properties of four robust estimators and three new robust statistics are introduced, and distributions of robust statistics are explored. Then, stopping rules and importance tests are modified. Finally, the performance of new method is shown and compared through simulation examples. Results indicate that the statistic constructed by Hodges-Lehmann and Shamos estimators clearly outperforms the others in efficiency and efficacy and without loss of robustness. In addition, empirical quantile of robust statistic is provided for performing screening in the case of small sample size.