DDHC: DD-HC test

In ddpca: Diagonally Dominant Principal Component Analysis

Description

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

Usage

DDHC(X, known_Sigma = NA, 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}(μ,Σ)
known_Sigma	The true covariance matrix of data. Default NA. If NA, then Σ will be estimated from data matrix X.
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). The use of H is not recommended as it's approximately valid only when p is sufficiently large and mean effect in alternative is really sparse.
HCT	DD-HC 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

IHCDD, 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 = DDHC(X,K = k)
print(results$H)
print(results$HCT)

ddpca documentation built on Sept. 15, 2019, 1:03 a.m.