STAB57H3 Lecture Notes - Lecture 26: Mean Squared Error, Consistent Estimator, Independent And Identically Distributed Random Variables
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The mean squared error of the estimator t of. The first term represents the variance of an estimator and the second term represents the bias. If for n the bias and variance both approaches 0 then the estimate is said to be consistent. An estimator tn is called mse consistent if. Mse(x ) =/n 0 as n . Therefore x is a mse consistent estimator of. In naive words, after you have calculated the mse of an estimator, just check if it goes to zero for large n Before making this claim, let us introduce a new notation and revisit few of the old ones. : the true value of the parameter which produced the data. (which is a unknown constant) Suppose (x1, x2, , xn) iid f (x. Claim: converges to 0 in probability (p. But we are going to skip the proof for now. Using inverse empirical cdf we can calculate the quantiles.
