Question

Let X1,X2,...,Xn denote independent and identically distributed random variables with variance 2. Which of the following is sucient to conclude that the estimator T = f(X1,...,Xn) of a parameter ✓ is consistent (fully justify your answer):

(a) Var(T)= $\frac{\sigma ^{2}}{n}$

(b) E(T)=$\frac{n}{n-1}\Theta$ and Var(T)= $\frac{\sigma ^{2}}{\sqrt{n}}$ .

(c) E(T)=$\theta$.

(d) E(T)=$\theta$ and Var(T)=$\sigma^{2}$

Answer 1

TOPIC:Sufficient condition for Consistency of an estimator.