MKendall (version 1.5-4)

MKER: Estimating Factor Numbers via Matrix Kendall's Tau Eigenvalue-Ratio Method

Description

This function is to estimate row and column factor numbers via Matrix Kendall's Tau Eigenvalue-Ratio Method.

Usage

MKER(X, kmax)

Value

khat

The estimated row factor number.

rhat

The estimated column factor number.

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.

kmax

The user-supplied maximum 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

fn=MKER(X,9)
fn$khat;
fn$rhat