What does the 'Consistency' of an estimator θ^n\hat{\theta}_nθ^n imply?
E[θ^n]=θE[\hat{\theta}_n] = \thetaE[θ^n]=θ
limn→∞P(∣θ^n−θ∣>ϵ)=0\lim_{n \to \infty} P(|\hat{\theta}_n - \theta| > \epsilon) = 0limn→∞P(∣θ^n−θ∣>ϵ)=0
limn→∞Var(θ^n)=0\lim_{n \to \infty} Var(\hat{\theta}_n) = 0limn→∞Var(θ^n)=0
The estimator is always unbiased