Matrix Kendall's tau in High-dimensions: A Robust Statistic for Matrix Factor Model (preprint)

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.

Infection probability under different air distribution patterns

Infectious diseases have caused significant physical harm to humans as well as enormous economic losses over the years. Effective ventilation and distribution of fresh air could help to reduce indoor cross-infection. The computational fluid dynamics (CFD) method was used in this paper to investigate airborne transmission with seven different air distribution methods. The revised Wells-Riley model, which took into account the non-uniform air distribution generated with the methods, was used to calculate the infection probability in an office room shared by ten occupants for 4 h. One of the occupants was an infector. The significance of the infector's location was studied. The obtained infection probability was compared to that obtained in the case of complete air mixing, which is uncommon in practice. Under specified conditions of this study, personalized ventilation (PV) performed the best in terms of preventing cross-infection, followed by displacement ventilation (DV), impinging jet ventilation (IJV), stratum ventilation (SV) and wall attachment ventilation (WAV). The number of infected occupants was reduced below the number obtained under the complete mixing assumption by using these air distribution methods. Mixing ventilation (MV) and diffuse ceiling ventilation (DCV) exhibited the worst performance. In comparison to the case of complete mixing the infection probability for seven out of nine susceptible occupants was higher with MV and for all occupants in the case of DCV. In SV, the position of the infector had a clear impact on the infection probability of susceptible individuals. WAV may perform better in practice if the system is well designed. The location of the exhaust outlets had a significant impact on the infection probability for DCV.