A Distribution-Free Test for Outliers

Determining whether a data set contains one or more outliers is a challenge commonly faced in applied statistics. This paper introduces a distribution-free test for multiple outliers in data drawn from an unknown data generating process. Besides, a sequential algorithm is proposed in order to identify the outlying observations in the sample. Our methodology relies on a two-stage nonparametric bootstrap procedure. Monte Carlo experiments show that the proposed test has good asymptotic properties, even for relatively small samples and heavy tailed distributions. The new outlier detection test could be instrumental in a wide range of statistical applications. The empirical performance of the test is illustrated by means of two examples in the fields of aeronautics and macroeconomics.