Decorrelation of Neutral Vector Variables: Theory and Applications
This work addresses a specific limitation in statistical analysis for non-Gaussian data, offering a novel solution that could benefit fields relying on multivariate decorrelation, though it appears incremental relative to existing decorrelation methods.
The paper tackles the problem of decorrelating non-Gaussian neutral vector variables by proposing two invertible nonlinear transformations, which successfully transform highly negatively correlated vectors into mutually independent scalar variables while preserving degrees of freedom, as verified using distance correlation measurements on Dirichlet-distributed data.
In this paper, we propose novel strategies for neutral vector variable decorrelation. Two fundamental invertible transformations, namely serial nonlinear transformation and parallel nonlinear transformation, are proposed to carry out the decorrelation. For a neutral vector variable, which is not multivariate Gaussian distributed, the conventional principal component analysis (PCA) cannot yield mutually independent scalar variables. With the two proposed transformations, a highly negatively correlated neutral vector can be transformed to a set of mutually independent scalar variables with the same degrees of freedom. We also evaluate the decorrelation performances for the vectors generated from a single Dirichlet distribution and a mixture of Dirichlet distributions. The mutual independence is verified with the distance correlation measurement. The advantages of the proposed decorrelation strategies are intensively studied and demonstrated with synthesized data and practical application evaluations.