Category:Definitions/Consistent Estimators
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This category contains definitions related to Consistent Estimators.
Related results can be found in Category:Consistent Estimators.
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 $\epsilon > 0$.
Pages in category "Definitions/Consistent Estimators"
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