Improving the Pe\~na-Prieto "KSD" procedure

Pe\~{n}a and Prieto (2007) proposed the "Kurtosis plus specific directions" (KSD) method for robust multivariate location and scatter estimation and outlier detection. Maronna and Yohai (2017) employed it as an initial estimator for multivariate S- and MM-estimators, and their simulations showed that KSD generally outperforms initial estimators based on subsampling. However further simulations show that KSD may become unstable and give wrong results in extreme situations when the contamination rate is "high" (>=0.2) and the ratio n/p of cases to variables is "low" (<10). Two simple modifications of the procedure are proposed, which greatly improve on the method's performance as an initial estimator, with only a small increase in computational time.