How to draw observations from a normal distribution and compute the mean using a customized estimator, and then running this procedure in a loop in r

Question

I want to use a custom estimator Yhat=(1/(n-4))*sum(Y_i) as an estimator for the mean of Y_i.

How do I draw, say, 20 observations from the distribution N(4,10) and compute the estimate of the sample mean using Yhat, and then repeat this procedure k amount of times in a loop and save the results in a matrix in r?

Answer 1

First, since you want the estimate of the mean, you don't need a matrix, a vector should be fine.

Yhat <- function(x) {
  if (length(x) <= 4) {
    stop("vector x must be at least 5 elements long")
  } else {
    sum(x) / (length(x) - 1)
  }
}  

k <- 100

result <- replicate(k, {
  simulations <- rnorm(20, 4, 10)
  Yhat(simulations)
})

result