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- rm(list = ls())
- rho <- 0.5
- sigma2 <- 1
- iters <- 10000
- cov <- rho * sqrt(sigma2)*sqrt(sigma2)
- Sigma <- matrix(cov, nrow = 2, ncol = 2)
- diag(Sigma) <- sigma2
- xs <- matrix(NA, nrow = iters, ncol = 2)
- for (i in 1:iters)
- {
- xs[i, ] <- MASS::mvrnorm(1, mu = rep(0, 2), Sigma = Sigma)
- }
- xc <- rnorm(iters, mean = 0, sd = sqrt(sigma2))
- cov_comp <- rho*sigma2+sigma2
- 2*sigma2+2*sigma2-2*cov_comp
- summary(apply(xs-xc, 1, var))
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