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highD2pop (version 1.0)

center: The centering value for the test statistic

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 $j=1,\dots,p$ 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

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

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