Frechet distance as a tool for diagnosing multivariate data Original Research Article

Outliers can have dramatic effects on results from statistical analyses and on conclusions based on statistical analyses. It is therefore important to detect outliers and influential points. Methods for detecting outliers in multivariate data may be based on assessments of changes in the estimate of the mean vector or changes in the estimate of the scatter matrix as data points are perturbed. Here we propose a method based on the Frechet distance between the observed empirical distributions of the unperturbed and perturbed data. As these distributions involve both the mean vector and the scatter matrix, the resulting diagnostics are functions of both mean and scatter. The proposed diagnostics are illustrated by two examples.