TOSI (version 0.3.0)

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

Description

Conduct the simultaneous inference for a set of loading vectors in the NUll hypothesises H01 that assumes the set of loading vectors are all zeroes.

Usage

FacRowMaxST(X, G1, q=NULL, Nsplit= 5, sub.frac=0.5,
              alpha=0.05, standardized=FALSE,seed=1)

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.

Arguments

X

a n-by-p matrix, the observed data

G1

a index set with values of components between 1 and p, the testing set in H01.

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.

Author

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
  G1 <- 1:10; # all are nonzero loading vectors
  FacRowMaxST(X, G1=G1, alpha=0.05, sub.frac=0.5)
  FacRowMaxST(X, q= 6, G1=G1, alpha=0.05, sub.frac=0.5) # specify the true number of factors
  # ex2: H01 is true
  G1 <- 481:500 # all are zero loading vectors
  FacRowMaxST(X, G1=G1, alpha=0.05, sub.frac=0.5)
  FacRowMaxST(X, q= 7, G1=G1, alpha=0.05, sub.frac=0.5) # specify a false number of factors