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G. Monti, K. Hron, P. Filzmoser, M. Templ:
"Covariance-Based Outlier Detection for Compositional Data with Structural Zeros: Application to Italian Survey of Household Income and Wealth Data";
in: "Dipartimento di Economia, Metodi Quantitativi e Strategie di Impresa", D. Vita e Pensiero (Hrg.); herausgegeben von: Vita e Pensiero; Vita e Pensiero, 2013, ISBN: 9788834325568.

Outlier detection is an important task for the statistical analysis of multivariate
data, because often the outliers contain important information about the
data structure. In compositional data, represented usually as proportions subject to
a unit sum constraint, the ratios between the parts (variables) contain the essential
information. The logratio approach is thus the logical approach which is also most
widely accepted. This inherent property is, however, incompatible with the presence
of zeros in compositions. Here we consider structural zeros, i.e., zeros that
are truly observed, and not zeros related to measurement errors (rounded zeros). In
order to identify possible outliers in compositional data with structural zeros, we
apply the Mahalanobis distance approach, where the key task is a robust estimation
of the covariance matrix. Only information from the non-zero parts of the compositions
is used to compute Mahalanobis distances, after the estimation of location
and covariance is performed in the imputation step of the algorithm. This resulting
outlier detection procedure is applied to the Italian Survey of Household Income
and Wealth (SHIW) data, collected by the Bank of Italy.

structural zeros; missing value imputation; Aitchison geometry on the simplex; Mahalanobis distance; variation matrix

http://boa.unimib.it/handle/10281/44960#.UqcrX6qnd3A