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Jun 26th, 2019
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  1. rm(list = ls())
  2.  
  3. rho <- 0.5
  4. sigma2 <- 1
  5. iters <- 10000
  6.  
  7. cov <- rho * sqrt(sigma2)*sqrt(sigma2)
  8. Sigma <- matrix(cov, nrow = 2, ncol = 2)
  9. diag(Sigma) <- sigma2
  10.  
  11. xs <- matrix(NA, nrow = iters, ncol = 2)
  12.  
  13. for (i in 1:iters)
  14. {
  15. xs[i, ] <- MASS::mvrnorm(1, mu = rep(0, 2), Sigma = Sigma)
  16. }
  17.  
  18. xc <- rnorm(iters, mean = 0, sd = sqrt(sigma2))
  19.  
  20. cov_comp <- rho*sigma2+sigma2
  21.  
  22. 2*sigma2+2*sigma2-2*cov_comp
  23.  
  24. summary(apply(xs-xc, 1, var))
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