Resumen de Monitoring robust estimates for compositional data
In a number of recent articles Riani, Cerioli, Atkinson and others advocate the technique of monitoring robust estimates computed over a range of key parameter values (Cerioli et al., 2018; Riani et al., 2019). Through this approach the diagnostic tools of choice can be tuned in such a way that highly robust estimators which are as efficient as possible are obtained. This approach is applicable to different robust multivariate estimates like S- and MM-estimates, MVE and MCD as well as to the Forward Search in which monitoring is part of the robust method. Key tool for detection of multivariate outliers and for monitoring of robust estimates are the scaled Mahalanobis distances and statistics related to these distances. However, the results obtained with this tool in case of compositional data might be unrealistic since compositional data contain relative rather than absolute information and need to be transformed to the usual Euclidean geometry before the standard statistical tools can be applied. Several specific transformations have been introduced, but Filzmoser and Hron (2008) show that the transformation with the best properties with respect to robust estimates and keeping invariant the Mahalanobis distances is the ilr (isometric log-ratio) transformation. To illustrate the problem of monitoring compositional data and to demonstrate the usefulness of monitoring in this case we start with a simple example and then analyze a real life data set presenting the technological structure of manufactured exports which, as an indicator of their quality, is an important criterion for understanding the relative position of countries measured by their industrial competitiveness. The analysis is conducted with the R package fsdaR, which makes the analytical and graphical tools provided in the MATLAB FSDA library available for R users.
