Consistent Estimator

Definition

Let

• $X$ : Random variable, with
  • $\Omega$ : Parameter space
  • cdf $F(x;\theta \in \Omega )$
• $X_1,\dots ,X_n$ : Random sample of $X$
• $T_n$ : Statistic

If

$$T_n\stackrel{P}{\to }\theta$$

Then we say $T_n$ is a consistent estimator of $\theta$