Intermediate Statistical Theory
Intermediate Statistical Theory
4. Let Xn denote a random variable with mean µ and variance b/np, where p >
0, µ and b are constants (not functions of n). prove that Xn converges in
probability to µ. (use Chebyshev’s inequality).
5. An estimator θ
ˆ
n is said to be squared-error consistent for θ if limn→∞E[(θ
ˆ
n−
θ)
2] = 0.
(a) Show that any squared-error consistent θ
ˆ
n is asymptotically unbiased.
(b) Show that any squared-error consistent θ
ˆ
n is consistent.
DETAILED ASSIGNMENT
