This article is a Preprint
Preprints are preliminary research reports that have not been certified by peer review. They should not be relied on to guide clinical practice or health-related behavior and should not be reported in news media as established information.
Preprints posted online allow authors to receive rapid feedback and the entire scientific community can appraise the work for themselves and respond appropriately. Those comments are posted alongside the preprints for anyone to read them and serve as a post publication assessment.
Matrix Kendall's tau in High-dimensions: A Robust Statistic for Matrix Factor Model (preprint)
arxiv; 2022.
Preprint
in English
| PREPRINT-ARXIV | ID: ppzbmed-2207.09633v1
ABSTRACT
In this article, we first propose generalized row/column matrix Kendall's tau for matrix-variate observations that are ubiquitous in areas such as finance and medical imaging. For a random matrix following a matrix-variate elliptically contoured distribution, we show 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. We perform eigenvalue decomposition to the generalized row/column matrix Kendall's tau for recovering the loading spaces of the matrix factor model. We also propose to estimate the pair of the factor numbers by exploiting the eigenvalue-ratios of the row/column matrix Kendall's tau. Theoretically, we derive the convergence rates of the estimators for loading spaces, factor scores and common components, and prove the consistency of the estimators for the factor numbers without any moment constraints on the idiosyncratic errors. Thorough simulation studies are conducted to show the higher degree of robustness of the proposed estimators over the existing ones. Analysis of a financial dataset of asset returns and a medical imaging dataset associated with COVID-19 illustrate the empirical usefulness of the proposed method.
Full text:
Available
Collection:
Preprints
Database:
PREPRINT-ARXIV
Main subject:
COVID-19
Language:
English
Year:
2022
Document Type:
Preprint
Similar
MEDLINE
...
LILACS
LIS