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MSE stands for Mean Squared Error. It is a measure of the performance of an estimate or prediction, equal to the mean squared difference between the observed values and the estimated / predicted values.

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Consistent estimator, that is not MSE consistent

Could somebody give me an illustrative example of a (simply) consistent estimator that is not MSE consistent? … : $\hat{\theta}_m$ is simply consistent estimator of parameter $\theta$ if $\forall \epsilon > 0$: $$\lim_{m \to \infty} \mathbb{P}[| \hat{\theta}_m - \theta | > \epsilon] = 0$$ $\hat{\theta}_m$ is MSE
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