Estimation in compositional data analysis

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Abstract
Compositional data arise naturally in several branches of science, including chemistry, geology, biology, medicine, ecology and manufacturing design. In chemistry, these constrained data seem to occur typically when raw data are normalized or when output is obtained from a constrained estimation procedure, such as might be used in a source apportionment problem. It is important not only for chemists to be aware that the usual multivariate statistical techniques are not applicable to constrained data, but also to have access to appropriate techniques as they become available. The currently available methodology is due principally to Aitchison and is based on log–normal models. This paper suggests new parametric and non‐parametric approaches to significantly improve the existing methodology. In the parametric setting, some recent work of Rayens and Srinivasan is extended and a practical regression model is proposed. In the development of the non‐parametric approach, minimum distance methods coupled with multivariate bootstrap techniques are used to obtain point and region estimators.