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NeymanScott.R
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NeymanScott.R
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# 3/15/2021 Shuowen Chen
# Neyman Scott example
# generate x_it ~ N(mu_i, sigma^2)
set.seed(88)
n <- 250
T <- 5
H <- 1
#mu_i <- 0.1 * seq(n)
mu_i <- rnorm(n, mean = 0, sd = 1)
sigma <- 2
dat <- matrix(0, nrow = n, ncol = T)
for (i in 1:n) dat[i, ] <- rnorm(T, mean = mu_i[i], sd = sigma)
# MLE estimate
hat_mui <- apply(dat, 1, mean)
hat_sigma <- sqrt(sum(sweep(dat, 1, hat_mui)^2)/(n*T))
# indirect inference procedure
sim_dat <- function(phi, unitfe){
# simulate data
dat <- matrix(0, nrow = n, ncol = T)
for (i in 1:n) dat[i, ] <- rnorm(T, mean = unitfe[i], sd = phi)
return(dat)
}
objective <- function(phi, H, alpha_hat, coef) {
coef_sim <- 0
for (h in 1:H) {
dats <- sim_dat(phi, alpha_hat)
s_mui <- apply(dats, 1, mean)
# MLE estimate
s_sigma <- sqrt(sum(sweep(dats, 1, s_mui)^2)/(n*T))
coef_sim <- coef_sim + s_sigma/H
}
return( sum( (coef - coef_sim)^2 ) )
}
est <- optimize(objective, c(0, 3), H, hat_mui, hat_sigma)
result <- list(true = sigma, mle = hat_sigma, ii = est$minimum, H = H)
print(result)