| AEB {OPTtesting} | R Documentation |
AEB
Description
Estimate the parameters in the three-part mixture
Usage
AEB(
Z,
Sigma,
eig = eigs_sym(Sigma, min(400, length(Z)), which = "LM"),
eig_tol = 1,
set_nu = c(0),
set1 = c(0:10) * 0.01 + 0.01,
set2 = c(0:10) * 0.01 + 0.01,
setp = c(1:7) * 0.1
)
Arguments
Z |
a vector of test statistics |
Sigma |
covariance matrix |
eig |
eig value information |
eig_tol |
the smallest eigen value used in the calulation |
set_nu |
a search region for nu_0 |
set1 |
a search region for tau_sqr_1 |
set2 |
a search region for tau_sqr_2 |
setp |
a search region for proportion |
Details
Estimate the parameters in the three-part mixture Z|\mu ~ N_p(\mu,\Sigma )
where \mu_i ~ \pi_0 \delta_ {\nu_0} + \pi_1 N(\mu_1, \tau_1^2) + \pi_2 N(\mu_2, \tau_2^2), i = 1, ..., p
Value
The return of the function is a list in the form of list(nu_0, tau_sqr_1, tau_sqr_2, pi_0, pi_1, pi_2, mu_1, mu_2, Z_hat).
nu_0, tau_sqr_1, tau_sqr_2: The best combination of (\nu_0, \tau_1^2, \tau_2^2) that minimize the total variance from the regions (D_{\nu_0}, D_{\tau_1^2}, D_{\tau_2^2}).
pi_0, pi_1, pi_2, mu_1, mu_2: The estimates of parameters \pi_0, \pi_1, \pi_2, \mu_1, \mu_2.
Z_hat: A vector of simulated data base on the parameter estimates.
Examples
p = 500
n_col = 10
A = matrix(rnorm(p*n_col,0,1), nrow = p, ncol = n_col, byrow = TRUE)
Sigma = A %*% t(A) +diag(p)
Sigma = cov2cor(Sigma) #covariance matrix
Z = rnorm(p,0,1) #this is just an example for testing the algorithm.
#Not true test statistics with respect to Sigma
best_set = AEB(Z,Sigma)
print(c(best_set$pi_0, best_set$pi_1, best_set$pi_2, best_set$mu_1, best_set$mu_2))
library(MASS)
######################################
#construct a test statistic vector Z
p = 1000
n_col = 4
pi_0 = 0.6
pi_1 = 0.2
pi_2 = 0.2
nu_0 = 0
mu_1 = -1.5
mu_2 = 1.5
tau_sqr_1 = 0.1
tau_sqr_2 = 0.1
A = matrix(rnorm(p*n_col,0,1), nrow = p, ncol = n_col, byrow = TRUE)
Sigma = A %*% t(A) +diag(p)
Sigma = cov2cor(Sigma) #covariance matrix
b = rmultinom(p, size = 1, prob = c(pi_0,pi_1,pi_2))
ui = b[1,]*nu_0 + b[2,]*rnorm(p, mean = mu_1,
sd = sqrt(tau_sqr_1)) + b[3,]*rnorm(p, mean = mu_2,
sd = sqrt(tau_sqr_2)) # actual situation
Z = mvrnorm(n = 1,ui, Sigma, tol = 1e-6, empirical = FALSE, EISPACK = FALSE)
best_set =AEB(Z,Sigma)
print(c(best_set$pi_0, best_set$pi_1, best_set$pi_2, best_set$mu_1, best_set$mu_2))