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Refers to an estimator of a population parameter that "hits the true value" on average. That is, a function of the observed data $\hat{\theta}$ is an unbiased estimator of a parameter $\theta$ if $E(\hat{\theta}) = \theta$. The simplest example of an unbiased estimator is the sample mean as an estimator of the population mean.

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Consistent estimator, that is not MSE consistent

I'm trying to understand the concept of consistency in point estimation. Could somebody give me an illustrative example of a (simply) consistent estimator that is not MSE consistent? Just a recall of …
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