RESISTANT AND TEST-BASED OUTLIER REJECTION - EFFECTS ON GAUSSIAN ONE-SAMPLE AND 2-SAMPLE INFERENCE

Resistant and sequential teal-based procedures for the detection of mu ltiple outliers are compared in Gaussian one- and two-sample problems. Subsequent to statistical rejection of putative outliers, operating c haracteristics of hypothesis tests applied to samples that are outlier -free may differ from their nominal values. Outlier rejection rules ma y be calibrated, however, to control the rate of erroneous outlier lab eling in pure Gaussian samples. The small-sample behavior of resistant location and scale estimators used in outlier detection is examined t hrough simulation, yielding new formulas for calibration of boxplot-ba sed and shorth-based outlier-rejection rules. Effects of different out lier criteria and calibration rubrics on postrejection hypothesis test s are compared in a variety of contamination settings and real-world e xamples. Tests conducted subsequent to calibrated rejection have appro ximately nominal operating characteristics whether or not outliers are present. The selection of an outlier criterion can have an impact on inference and thus becomes a potential component of model uncertainty. Properly calibrated tools should be widely available so that this com ponent of uncertainty becomes better understood; we describe public-do main software implementing a variety of detection techniques.