Title: Monitoring robust estimates for compositional data
Authors: Valentin Todorov - UNIDO (Austria) [presenting]
Abstract: The monitoring of robust estimates computed over a range of key parameter values is a recent technique. 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. 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. Compositional data are closed data, i.e. they sum up to a constant value (1 or 100 per cent or any other constant). This constraint makes it necessary to find a transformation of the data from the so called simplex sample space to the usual real space. To illustrate the problem of monitoring compositional data 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 already available in the MATLAB FSDA library available for R users.