Properties Of Estimators

Question 1

What is sampling distribution of an estimator T(X1,…,Xn)

Answer 1

Sampling distribution of an estimator T(X1,…,Xn) is the distribution of RV T which follows from definition of T and joint distribution of X1,…Xn

Question 2

What is the bias of an estimator T(X1,…Xn) of theta and when is an estimator unbiased

Answer 2

Bias of an estimator T(X1,…,Xn) of theta is:
Bias(T) = E(T) - theta
An estimator is unbiased when :
E(T) = theta for all theta

Question 3

What is precision of an estimator T(X1,…,Xn) of theta

Answer 3

Precision of an estimator T(X1,…,Xn) of theta is:

Precision(T) = 1/Var(T)

Question 4

What is mean square error of an estimator T(X1,…,Xn) of theta

Answer 4

Mean square error of an estimator T(X1,…,Xn) of theta is:

MSE(T) = E{(T-THETA)^2} = Var(T) + 0 + (bias(T))^2