IHCDD {ddpca}

IHC-DD test

Description

Combining Innovated Higher Criticism with DDPCA for detecting sparse mean effect.

Usage

IHCDD(X, method = "nonconvex", K = 1, lambda = 3, max_iter_nonconvex = 15, 
SDD_approx = TRUE, max_iter_SDD = 20, eps = NA, rho = 20, max_iter_convex = 50, 
alpha = 0.5, pvalcut = NA)

Arguments

X

A n\times p data matrix, where each row is drawn i.i.d from \mathcal{N}(\mu,\Sigma)

method

Either "convex" or "noncovex", indicating which method to use for DDPCA.

K

Argument in function DDPCA_nonconvex. Need to be specified when method = "nonconvex"

lambda

Argument in function DDPCA_convex. Need to be specified when method = "convex"

max_iter_nonconvex

Argument in function DDPCA_nonconvex.

SDD_approx

Argument in function DDPCA_nonconvex.

max_iter_SDD

Argument in function DDPCA_nonconvex.

eps

Argument in function DDPCA_nonconvex.

rho

Argument in function DDPCA_convex.

max_iter_convex

Argument in function DDPCA_convex.

alpha

Argument in function HCdetection.

pvalcut

Argument in function HCdetection.

Details

See reference paper for more details.

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). Not recommended for use.

HCT

IHC-DD Test statistic

Author(s)

Fan Yang <[e-mail]>

References

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

See Also

DDHC, HCdetection, DDPCA_convex, DDPCA_nonconvex

Examples

library(MASS)
n = 200
p = 200
k = 3
rho = 0.5
a = 0:(p-1)
Sigma_mu = rho^abs(outer(a,a,'-'))
Sigma_mu = (diag(p) + Sigma_mu)/2 # Now Sigma_mu is a symmetric diagonally dominant matrix
B = matrix(rnorm(p*k),nrow = p)
Sigma = Sigma_mu + B %*% t(B)
X = mvrnorm(n,rep(0,p),Sigma)
results = IHCDD(X,K = k)
print(results$H)
print(results$HCT)