{'fraction_non_alphanumeric': 0.015006821282401092, 'fraction_numerical': 0.002728512960436562, 'mean_word_length': 5.35064935064935, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A performance study for multivariate location and shape estimators

Exploratory data‐analysis methods and empirical model‐building techniques often attempt to determine the center and spread of multivariate data in order to determine the relative location of observations. The most common measure of multivariate location is the Mahalanobis distance. This measure uses standard mean and covariance matrix estimators for the center and spread. Outliers tend to influence these standard measures such that the corresponding Mahalanobis distances are inappropriately large for data near the true centroid, and relatively small for true outliers. As such, robust measures of location and spread are needed. Many robust measures have been proposed including the minimum covariance determinant, and the minimum volume ellipsoid. It is not clear how these methods perform under various data settings. We perform a comprehensive evaluation of the most referenced methods from the literature. A Monte Carlo simulation study is used to generate data without outliers and data with outliers dispersed separately and in groups or clouds. The methods are evaluated in terms of their ability to detect outliers and their ability not to signal false alarms for clean data. The findings from the study indicate that, although several methods display consistently solid performance, the method of Rocke and Woodruff performs the overall best. Copyright © 2002 John Wiley & Sons, Ltd.