Question

Statistics question. Please, help
Estimate \(\mu\)
\(X_i\)~ \(N(\mu, \sigma^2)\)
\(\hat\mu=\dfrac{X_1+\cdots+X_n}{n}\)

Answer 1

What is \(N\)

Answer 2

In class, my Prof did
\(E(\hat\mu)= \mu\) I understood it.
\(Var(\hat\mu)=\dfrac{\sigma^2}{n}\). I understood it also
And then
\(B_\mu \hat\mu =\mu-\mu =0\) I got it also
Then
\(MSE_\mu \hat\mu= Var(\hat\mu)+B_\mu \hat\mu = \dfrac{\sigma^2}{n}\)

Answer 3

And said, as n goes to infinitive, MSE goes to 0. and done

Answer 4

I don't get why he stopped there. The question is about estimate \(\mu\), I didn't see it at the end.

Answer 5

@Zarkon

Answer 6

If I understand well, the MSE goes to 0 when we have an infinite amount of samples (n goes to infinitive). And, in this case, we can say that the estimator û predicts observations of the parameter μ with perfect accuracy (i.e we can estimate μ by û).

Answer 7

Thanks for explanation.

Answer 8

Welcome !

Answer 9

In your book...loot at definition 9.2 and theorem 9.1 on page 450

Answer 10

It means we use this method to consider whether \(\hat\mu\) is consistence or not, right?