Testing the equality of high dimensional mean vector to zero using the method developed in arXiv:1406.1939 [math.ST]
oneMean(X, m = 2500, filter = TRUE, S = NULL, alpha = 0.05, DNAME)The \(n x p\) data matrix.
The number of Monte-Carlo samples in the test, default to be \(2500\)
A logical indicator of the filtering process, defaul to be TRUE
Covariance matrix of \(X\), if not presented it will be estimated from the input sample.
The significant level of the test.
Defaul input.
Value of testing statistics, p-values (the non-studentized statistic and the studentized statistic respectively), alternative hypothesis, and the name of testing procedure.
Implement the method developed in arXiv:1406.1939 [math.ST] to test whether a high dimensional mean vector is zero or not, which is equivalent to test \(H_0: \mu=\mu_0\) for some prescribed value \(\mu_0\) which can be subtracted from the data. The procedure utilizes bootstrap concept and derive the critical values using independent Gaussian vectors whose covariance is estimated using sample covariance matrix.
J. Chang, W. Zhou and W.-X. Zhou, Simulation-Based Hypothesis Testing of High Dimensional Means Under Covariance Heterogeneity (2014), arXiv:1406.1939.