MKER {MKendall}

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)

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.

Details

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

Value

khat

The estimated row factor number.

rhat

The estimated column factor number.

Author(s)

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

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