Large-scale matrix-variate data have been widely observed nowadays in various research areas such as finance, signal processing and medical imaging. Modelling matrix-valued data by matrix-elliptical family not only provides a flexible way to handle heavy-tail property and tail dependencies, but also maintains the intrinsic row and column structure of random matrices. We proposed a new tool named matrix Kendall's tau which is efficient for analyzing random elliptical matrices. By applying this new type of Kendell’s tau to the matrix elliptical factor model, we propose a Matrix-type Robust Two-Step (MRTS) method to estimate the loading and factor spaces. See the details in He at al. (2022) <arXiv:2207.09633>. In this package, we provide the algorithms for calculating sample matrix Kendall's tau, the MRTS method and the Matrix Kendall's tau Eigenvalue-Ratio (MKER) method which is used for determining the number of factors.

Calculation routines based on the FOCUS Kinetics Report (2006,
  2014).  Includes a function for conveniently defining differential equation
  models, model solution based on eigenvalues if possible or using numerical
  solvers.  If a C compiler (on windows: 'Rtools') is installed, differential
  equation models are solved using automatically generated C functions.
  Non-constant errors can be taken into account using variance by variable or
  two-component error models <doi:10.3390/environments6120124>.  Hierarchical
  degradation models can be fitted using nonlinear mixed-effects model packages
  as a back end <doi:10.3390/environments8080071>.  Please
  note that no warranty is implied for correctness of results or fitness for a
  particular purpose.

Computation of various confidence intervals (Altman et al. (2000), ISBN:978-0-727-91375-3; Hedderich and Sachs (2018), ISBN:978-3-662-56657-2) including bootstrapped versions (Davison and Hinkley (1997), ISBN:978-0-511-80284-3) as well as Hsu (Hedderich and Sachs (2018), ISBN:978-3-662-56657-2), permutation (Janssen (1997), <doi:10.1016/S0167-7152(97)00043-6>), bootstrap (Davison and Hinkley (1997), ISBN:978-0-511-80284-3), intersection-union (Sozu et al. (2015), ISBN:978-3-319-22005-5) and multiple imputation (Barnard and Rubin (1999), <doi:10.1093/biomet/86.4.948>) t-test; furthermore, computation of intersection-union z-test as well as multiple imputation Wilcoxon tests. Graphical visualizations: volcano plot, Bland-Altman plots (Bland and Altman (1986), <doi:10.1016/S0140-6736(86)90837-8>; Shieh (2018), <doi:10.1186/s12874-018-0505-y>), mean difference plot (Boehning et al. (2008), <doi:10.1177/0962280207081867>), plot of test statistic for permutation and bootstrap tests as well as objects of class htest.