A kernel density approach for replacing rounded zeros in compositional data sets

Abstract

The logratio methodology widely used in compositional data analysis is not applicable when some components have rounded zeros. There are many univariate and multivariate methods that have been used to deal with rounded zeros. However, both of them have restrictions: the univariate methods replaced the rounded zeros only using the information of the corresponding component; the multivariate methods need to assume the distribution of transformed data. When the form of the distribution function is unknown, a multivariate nonparametric replacement approach is proposed in this paper. The proposed method uses conditional expected value based on isometric logratio coordinates to replace rounded zeros, in which the conditional density is estimated through multivariate Gauss kernel function. The permutation invariance and invariance under change of orthonormal basis are also presented. Simulation studies show that the proposed method has better performance than previous methods as the percentage of rounded zeros increases. The proposed method is also applied on the moss data from the Kola project.

Keywords

• Compositional data,Isometric logratio coordinates,Rounded zeros,Gauss kernel function,Detection limit

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