center: The centering value for the test statistic

In highD2pop: Two-Sample Tests for Equality of Means in High Dimension

Description

This is a helper function for the generalized component test from Gregory et al. (2014) which computes and returns the value 1 + \hat{c}_{jn}/n + \hat{d}_{jn}/n^2 for a component j. The GCT.test and GCT.sim average these values across j=1,…,p to obtain the centering 1 + \hat{a}_{n}/n + \hat{b}_{n}/n^2 for the generalized component test statistic.

Usage

center(xy,n,m,ntoorderminus=2)

Arguments

xy	a vector of length n + m containing the concatenation of the n realizations of a given component from the first sample and the m realizations of the same component from the second sample.
n	the number of entries in xy belonging to the first sample.
m	the number of entries in xy belonging to the second sample.
ntoorderminus	the order of terms retained in 1 + \hat{c}_{jn}/n + \hat{d}_{jn}/n^2. If ntoorderminus=0, then 1 is returned. If ntoorderminus=1 then 1 + \hat{c}_{jn}/n is returned. If ntoorderminus=2 then 1 + \hat{c}_{jn}/n+\hat{d}_{jn}/n^2 is returned.

Value

A scalar equal to 1, 1 + \hat{c}_{jn}/n , or 1 + \hat{c}_{jn}/n+\hat{d}_{jn}/n^2 , respectively, for ntoorderminus=0,1,2.

Author(s)

Karl Gregory [e-mail], http://www.stat.tamu.edu/~kbgregory.

References

Gregory, K., Carroll, R. J., Baladandayuthapani, V. and Lahiri, S. (2015). A two-sample test for equality of means in high dimension. Journal of the American Statistician, to appear

highD2pop documentation built on May 2, 2019, 5:11 a.m.