Definition:Consistent Estimator
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Definition
Let $X_1, X_2, \ldots, X_n$ be random variables.
Let the joint distribution of $X_1, X_2, \ldots, X_n$ be indexed by a population parameter $\theta$.
Let $\hat \theta$ be an estimator of $\theta$.
Then $\hat \theta$ is consistent if and only if:
- $\ds \lim_{n \mathop \to \infty} \map \Pr {\size {\hat \theta - \theta} \ge \epsilon} = 0$
for all $\epsilon > 0$.
Also see
- Results about consistent estimators can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): consistent estimator
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): estimator
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): consistent estimator
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): estimator