MKendall (version 1.5-4)

MRTS: Matrix Robust Two-Step Algorithm for Large-Dimensional Matrix Elliptical Factor Model

Description

This function is to fit the large-dimensional matrix elliptical factor model via the Matrix Robust Two-Step (RTS) algorithm.

Usage

MRTS(X, k, r)

Value

The return value is a list. In this list, it contains the following:

Rloading

The estimated row loading matrix of dimension \(p \times k\)

Cloading

The estimated column loading matrix of dimension \(q \times r\)

Fhat

The estimated factor matrices, are output in the form of a three-dimensional array with dimensions of \(T \times k \times r\). \(T\) is the sample size, \(k\) and \(r\) are the row and column dimensions of each factor matrix, respectively.

Arguments

X

Input three-dimensional array, of dimension \(T \times p \times q\). \(T\) is the sample size, \(p\) is the row dimension of each matrix observation and \(q\) is the column dimension of each matrix observation.

k

A positive integer indicating the row factor numbers.

r

A positive integer indicating the column factor numbers.

Author

Yong He, Yalin Wang, Long Yu, Wang Zhou and Wenxin Zhou.

Details

See He at al. (2022) <arXiv:2207.09633> for details.

References

He, Y., Wang, Y., Yu, L., Zhou, W., & Zhou, W. X. (2022). A new non-parametric Kendall's tau for matrix-value elliptical observations <arXiv:2207.09633>.

Examples

set.seed(123456)
T=20;p=10;q=10;k=2;r=2
R=matrix(runif(p*k,min=-1,max=1),p,k)
C=matrix(runif(q*r,min=-1,max=1),q,r)
  X=Y=E=array(0,c(T,p,q))
    for(i in 1:T){
      Y[i,,]=R%*%matrix(rnorm(k*r),k,r)%*%t(C)
      E[i,,]=matrix(rnorm(p*q),p,q)
    }
    X=Y+E

fit=MRTS(X,k,r)
fit$Rloading;fit$Cloading;fit$Fhat