Nothing
# Formulas under (3)
alpha_star_n_BOP19 <- function(y_n_aver, Sigma_n_inv, mu_n, mu_0) {
numerator <- t(y_n_aver) %*% Sigma_n_inv %*% mu_n %*%
t(mu_0) %*% Sigma_n_inv %*% mu_0-
t(mu_n) %*% Sigma_n_inv %*% mu_0 %*%
t(y_n_aver) %*% Sigma_n_inv %*% mu_0
denomen <- t(y_n_aver) %*% Sigma_n_inv %*% y_n_aver %*%
t(mu_0) %*% Sigma_n_inv %*% mu_0-
(t(y_n_aver) %*% Sigma_n_inv %*% mu_0)^2
as.numeric(numerator / denomen)
}
beta_star_n_BOP19 <- function(y_n_aver, Sigma_n_inv, mu_n, mu_0) {
numerator <- t(y_n_aver) %*% Sigma_n_inv %*% y_n_aver %*%
t(mu_n) %*% Sigma_n_inv %*% mu_0-
t(y_n_aver) %*% Sigma_n_inv %*% mu_0 %*%
t(y_n_aver) %*% Sigma_n_inv %*% mu_n
denomen <- t(y_n_aver) %*% Sigma_n_inv %*% y_n_aver %*%
t(mu_0) %*% Sigma_n_inv %*% mu_0-
(t(y_n_aver) %*% Sigma_n_inv %*% mu_0)^2
as.numeric(numerator / denomen)
}
# From Theorem 1
alpha_star_BOP19 <- function(c, mu_n, Sigma_n_inv, mu_0) {
I1 <- t(mu_n) %*% Sigma_n_inv %*% mu_n
I2 <- t(mu_0) %*% Sigma_n_inv %*% mu_0
I3 <- t(mu_n) %*% Sigma_n_inv %*% mu_0
numerator <- I1*I2 - I3^2
I4 <- t(mu_n) %*% Sigma_n_inv %*% mu_n
I5 <- t(mu_0) %*% Sigma_n_inv %*% mu_0
I6 <- t(mu_n) %*% Sigma_n_inv %*% mu_0
denomen <- (c+I4)*I5 - I6^2
as.numeric(numerator / denomen)
}
beta_star_BOP19 <- function(alpha_star, mu_n_t, Sigma_n_inv, mu_0) {
I1 <- mu_n_t %*% Sigma_n_inv %*% mu_0
I2 <- t(mu_0) %*% Sigma_n_inv %*% mu_0
II <-I1 / I2
as.numeric((1-alpha_star)*II)
}
# From Theorem 3
alpha_star_hat_BOP19 <- function(n, p, y_n_aver, Sigma_n_inv, mu_0) {
I1 <- t(y_n_aver) %*% Sigma_n_inv %*% y_n_aver - p/(n-p)
I2 <- t(mu_0) %*% Sigma_n_inv %*% mu_0
I3 <- t(y_n_aver) %*% Sigma_n_inv %*% mu_0
numerator <- I1*I2 - I3^2
I4 <- t(y_n_aver) %*% Sigma_n_inv %*% y_n_aver
I5 <- t(mu_0) %*% Sigma_n_inv %*% mu_0
I6 <- t(y_n_aver) %*% Sigma_n_inv %*% mu_0
denomen <- I4*I5 - I6^2
as.numeric(numerator / denomen)
}
beta_star_hat_BOP19 <- function(n, p, alpha_star_hat,
y_n_aver_t, Sigma_n_inv, mu_0) {
I1 <- y_n_aver_t %*% Sigma_n_inv %*% mu_0
I2 <- t(mu_0) %*% Sigma_n_inv %*% mu_0
II <-I1 / I2
as.numeric((1-alpha_star_hat)*II)
}
# From Theorem 4
s_BOP19 <- function(mu_0, Sigma_n_inv, mu_n){
I1 <- t(mu_n) %*% Sigma_n_inv %*% mu_n
I2 <- (t(mu_0) %*% Sigma_n_inv %*% mu_n)^2
I3 <- t(mu_0) %*% Sigma_n_inv %*% mu_0
as.numeric(I1 - I2/I3)
}
R_BOP19 <- function(mu_0, Sigma_n_inv, mu_n){
I1 <- t(mu_0) %*% Sigma_n_inv %*% mu_n
I2 <- t(mu_0) %*% Sigma_n_inv %*% mu_0
as.numeric(I1 / I2)
}
sigma_s_square_BOP19 <- function(c, s) 2*(c+2*s) + 2/(1-c)*(c+s)^2
Omega_BOP19 <- function(c, sigma_s_square, Sigma_n_inv, mu_0, s, R){
El11 <- c^2 * sigma_s_square / (c + s)^4
El12 <- El21 <- c^2 * sigma_s_square * R / (c + s)^4
El22 <- c^2 * sigma_s_square * R^2 / (c + s)^4 +
c^2 * (c + s)^(-2) * (1 + (c + s)/(1-c)) /
as.numeric(t(mu_0) %*% Sigma_n_inv %*% mu_0)
matrix(data = c(El11, El12, El21, El22), 2, 2)
}
Any scripts or data that you put into this service are public.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.