Karel Hron (Palacky University), “Classical and robust statistical analysis of compositional data”, Statistics Seminar, Toulouse: TSE, December 7, 2010, 14:00–15:30, room MH 203.
Many practical data sets in official statistics, environmental science and various other disciplines including economical applications are in fact compositional data because only the ratios between the variables are informative, e.g., household expenditures on various costs from the monthly budget. Such kind of data is usually represented by proportions or percentages. Compositional data follow the Aitchison geometry on the simplex, and for applying statistical methods designed for the Euclidean geometry they need to be transformed first using a proper logratio transformation. The isometric logratio (ilr) transformation has the best geometrical properties, and it avoids the singularity problem introduced by the centered logratio (clr) transformation. Robust multivariate methods which are based on a robust covariance estimation can thus only be used with ilr transformed data. We show for different multivariate methods, often used also in economical applications, like outlier detection, principal component analysis, discriminant or regression analysis, how they can be managed for compositional data, and provide algorithms for the computation.