How To Find Estimator Is Consistent. Show that the sample mean is a consistent estimator of the population mean. This notion is equivalent to convergence in probability defined below.
In our first example, we found if x 1,.,x n ∼ n(θ,1), then the mse of ¯x is 1/n. Here's one way to do it: A consistent estimator in statistics is such an estimate which hones in on the true value of the parameter being estimated more and more accurately as the sample size increases.
