l_value {OPTtesting}

l_value

Description

Calculating the estimates for P(\mu_i \ge 0 | Z)

Usage

l_value(
  Z,
  Sigma,
  best_set = AEB(Z, Sigma),
  eig = eigs_sym(Sigma, min(400, length(Z)), which = "LM"),
  sim_size = 3000,
  eig_value = 0.35
)

Arguments

Z

a vector of test statistics

Sigma

covariance matrix

best_set

a list of parameters (list(nu_0 = ..., tau_sqr_1 = ..., tau_sqr_2 = ..., pi_0 = ..., pi_1= ..., pi_2 = ..., mu_1 = ..., mu_2 = ...)) or returns from Fund_parameter_estimation

eig

eig value information

sim_size

simulation size

eig_value

the smallest eigen value used in the calulation

Value

a vector of estimates for P(\mu_i \ge 0 | Z)

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
 l_value(Z,Sigma,sim_size = 5)
 #To save time, we set the simulation size to be 10, but the default value is much better.

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)

l_value(Z,Sigma)