Comparison studies of tin deposits (Priamurye, Russia) using the Aitchison’s methodology

A study of tin deposits from Priamurye (Russia) is performed to analyze the differences between them based on their origin and also on commercial criteria. A particular analysis based on their vertical zonality is also given for samples from Solnechnoe deposit. All the statistical analysis are made on the subcomposition formed by seven trace elements in cassiterite (In, Sc, Be, W, Nb, Ti and V) using the Aitchison’ methodology of analysis of compositional data

A comparison of the alr and ilr transformations for kernel density estimation of compositional data

In a seminal paper, Aitchison and Lauder (1985) introduced classical kernel density estimation techniques in the context of compositional data analysis. Indeed, they gave two options for the choice of the kernel to be used in the kernel estimator. One of these kernels is based on the use the alr transformation on the simplex SD jointly with the normal distribution on RD-1. However, these authors themselves recognized that this method has some deficiencies. A method for overcoming these dificulties based on recent developments for compositional data analysis and multivariate kernel estimation theory, combining the ilr transformation with the use of the normal density with a full bandwidth matrix, was recently proposed in Martín-Fernández, Chacón and Mateu- Figueras (2006). Here we present an extensive simulation study that compares both methods in practice, thus exploring the finite-sample behaviour of both estimators