ddpca (version 1.1)

HCdetection: Higher Criticism for detecting rare and weak signals

Description

This function takes a bunch of p-values as input and ouput the Higher Criticism statistics as well as the decision (rejection or not).

Usage

HCdetection(p, alpha = 0.5, pvalcut = NA)

Arguments

p

A vector of size n containing p-values from data

alpha

A number between 0 and 1. The smallest alpha*n p-values will be used to calculate the HC statistic. Default is 0.5.

pvalcut

A number between 0 and 1. Those small p-values (smaller than pvalcut) will be taken away to avoid heavy tails of test statistic. Set it to NA is equivalent to setting it to \(1/n\).

Value

Returns a list containing the following items

H

0 or 1 scalar indicating whether \(H_0\) the global null is rejected (1) or not rejected (0)

HCT

Higher Criticism test statistic

%% ...

Details

This function is an adaptation of the Matlab code here http://www.stat.cmu.edu/~jiashun/Research/software/HC/

References

Donoho, D. and Jin, J., Higher criticism for detecting sparse heterogeneous mixtures. Ann. Statist. 32 (2004), no. 3, 962--994.

Ke, Z., Xue, L. and Yang, F., 2019. Diagonally Dominant Principal Component Analysis. Journal of Computational and Graphic Statistics, under review.

Examples

# NOT RUN {
n = 1e5
data = rnorm(n)
p = 2*(1 - pnorm(abs(data)))
result = HCdetection(p)
print(result$H)
print(result$HCT)
# }