RegMax: Data splitting-based two-stage maximum testing method for the...

In TOSI: Two-Directional Simultaneous Inference for High-Dimensional Models

Data splitting-based two-stage maximum testing method for the regression coefficients in linear regression models

Description

Conduct the simultaneous inference for a set of regression coefficients in the null hypothesises H01 that assume the set of regression coefficients components are all zeroes.

Usage

  RegMax(X, Y,  G1, 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 response vector.
G1	a positive vector with values between 1 and p, the set of H01.
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 <- 50; 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
    RegMax(dat1$X, dat1$Y, 1:p)
    # ex1: H01 is true
    RegMax(dat1$X, dat1$Y, p)
  

TOSI documentation built on Feb. 16, 2023, 7:46 p.m.