ITP_proj {OLCPM}

testing the number of row factors- with projection

Description

This function tests whether the number of row factors is equal or larger than a given integer, under a two-way factor model, using projected version of sample covariance.

Usage

ITP_proj(
  Y,
  k = 1,
  alpha = 0.05,
  kmax = 4,
  epsilon = 0.05,
  r = 8,
  M = 100,
  S = 100,
  fq = 1/4
)

Arguments

Y

data, a T\times p1\times p2 array.

k

an positive integer indicating which eigenvalue to test.

alpha

a number in (0,1), indicating the significance of the test.

kmax

a positive integer smaller than p2, indicating the upper bound for the factor numbers, and the dimension of projection matrix.

epsilon

a small positive number in (0,1), indicating the size of scaling.

r

a positive number indicating the order of the power function for transforming the rescaled eigenvalue.

M

a large integer for the number of Gaussian variables in the randomized test.

S

another large integer for the number of replications in the strong rule. Usually M=S=T.

fq

a number in (0,0.5), controlling the threshold function of the strong rule.

Details

See He et al. (2023)

Value

a logical value. 1 for "the number of row factors is smaller than k". 0 for "at least k row factors exists".

References

He Y, Kong X, Trapani L, & Yu L (2023). One-way or two-way factor model for matrix sequences? Journal of Econometrics, 235(2), 1981-2004.

Examples

k1=3
k2=3
Sample_T=100
p1=40
p2=20

Y=gen.data(Sample_T,p1,p2,k1,k2,tau=0.5,change=0)
ITP_proj(Y,k=1,M=Sample_T,S=Sample_T)
ITP_proj(Y,k=4,M=Sample_T,S=Sample_T)