FacRowMinST {TOSI}

Data splitting-based two-stage minimum testing method for a group of loading vectors in factor models.

Description

Conduct the simultaneous inference for a set of loading vectors inr the NUll hypothesises H02 that assumes there is zero loading vector in the set of loading vectors.

Usage

  FacRowMinST(X, G2,  q=NULL, Nsplit= 5, sub.frac=0.5,
              alpha=0.05, standardized=FALSE,seed=1)

Arguments

X

a n-by-p matrix, the observed data

G2

a positive vector with values between 1 and p, the set of H02.

q

a positive integer, the number of factors. It will automatically selected by a criterion if it is NULL.

Nsplit

a positive integer, the number of data spliting, default as 5.

sub.frac

a positive number between 0 and 1, the proportion of the sample used in stage I.

alpha

a positive real, the significance level.

standardized

a logical value, whether use the standardized test statistic.

seed

a non-negative integer, the random seed.

Value

return a vector with names 'CriticalValue', 'TestStatistic', 'reject_status', 'p-value' if Nsplit=1, and 'reject_status' and 'adjusted_p-value' if Nsplit>1.

Note

nothing

Author(s)

Liu Wei

References

Wei Liu, Huazhen Lin, Jin Liu (2020). Estimation and inference on high-dimensional sparse factor models.

See Also

Factorm

Examples

  ### Example
  dat <- gendata_Fac(n = 300, p = 500)
  res <- Factorm(dat$X)
  X <- dat$X
  # ex1: H01 is false
  G2 <- 1:200; # all are nonzero loading vectors
  FacRowMinST(X, G2=G2, alpha=0.05, sub.frac=0.5)
  FacRowMinST(X, q= 6, G2=G2, alpha=0.05, sub.frac=0.5) # specify the true number of factors
  # ex2: H01 is true
  G2 <- 1:500 # all are zero loading vectors
  FacRowMinST(X, G2=G2, alpha=0.05, sub.frac=0.5)
  FacRowMinST(X, q= 7, G2=G2, alpha=0.05, sub.frac=0.5) # specify a false number of factors