A0921
Title: A new non-parametric Kendall's tau for matrix-valued elliptical observations
Authors: Yong He - Shandong University (China) [presenting]
Abstract: The aim is to propose a new non-parametric Kendall's tau for matrix-variate observations that are ubiquitous in areas such as finance and medical imaging, named row/column matrix Kendall's tau. For a random matrix following the matrix-variate elliptically contoured distribution, it is shown that the eigenspaces of the proposed row/column matrix Kendall's tau coincide with those of the row/column scatter matrix respectively, with the same descending order of the eigenvalues. To show the usefulness of the new non-parametric Kendall's tau, the focus is on a two-way dimension reduction model, namely the growing popular "matrix factor model" in the literature. Eigenvalue decomposition is performed on the generalized row/column matrix Kendall's tau to recover the loading spaces of the matrix factor model. Estimating the pair of factor numbers is also proposed by exploiting the eigenvalue ratios of the row/column matrix Kendall's tau. Theoretically, the convergence rates of the estimators are derived for loading spaces, factor scores and common components without any moment constraints on the idiosyncratic errors. Bahadur representation for the estimated loadings is also provided. The proposed methods can further be generalized to analyze high-order tensors. Thorough simulation studies are conducted to show a higher degree of robustness of the proposed estimators than the existing ones.
