RegMin {TOSI}

Data splitting-based two-Stage minimum testing method for the regression coefficients in linear regression models.

Description

Conduct the simultaneous inference for a set of regression coefficients in a null hypothesises H02 that assumes the set of regression coefficients components exist zero.

Usage

  RegMin(X, Y,  G2, Nsplit = 5, sub.frac=0.5, alpha=0.05, seed=1,  standardized=FALSE)

Arguments

X

a n-by-p matrix, the observed covariates matrix.

Y

a n-dimensional vector, the observed outcome vector.

G2

a positive vector with values between 1 and p, the set of regression coefficients in the null hypothesises H02.

Nsplit

a positive integer, the random split times used, default as 5.

sub.frac

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

alpha

a positive real, the significance level.

seed

a non-negative integer, the random seed.

standardized

a logical value, whether standerdize the covariates matrix in the stage I.

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

Liu, W., Lin, H., Liu, J., & Zheng, S. (2020). Two-directional simultaneous inference for high-dimensional models. arXiv preprint arXiv:2012.11100.

See Also

gendata_Reg

Examples

  
  ### Example
  n <- 100; p <- 20;i <- 1
  s0 <- 5 # First five components are nonzeros
  rho <- 1;
  dat1 <- gendata_Reg(n, p, s0, seed=i, rho)
  # ex1: H01 is false
  RegMin(dat1$X, dat1$Y, 1:s0)
  # ex1: H01 is true
  RegMin(dat1$X, dat1$Y, p)