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According to the wikipedia page at http://en.wikipedia.org/wiki/Mean_squared_error, it has:

Note that, although the MSE is not an unbiased estimator of the error variance, it is consistent, given the consistency of the predictor.

However, I saw from literature that MSE is indeed an unbiased estimator to the variance. My textbook does say it's an unbiased estimator. Is the wikipedia correct?

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    $\begingroup$ Exactly what "literature" are you referring to? $\endgroup$
    – whuber
    Nov 30 '14 at 17:33
  • $\begingroup$ @whuber I was referring to my books. They are state MSE is an unbiased estimator, not consistent. $\endgroup$
    – SmallChess
    Nov 30 '14 at 23:44
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    $\begingroup$ "Your books", unfortunately, means nothing to us--we have no idea what they might be. It is possible you are not fully or accurately characterizing what is in them, which is why it could be helpful to know which ones they are. $\endgroup$
    – whuber
    Dec 1 '14 at 0:47
  • $\begingroup$ MSE can be bias or unbias, there are equations for both. I'd recommend reading I'd recommend reading this for more clarity math.arizona.edu/~jwatkins/n-unbiased.pdf. $\endgroup$
    – Lauren
    Apr 5 '18 at 1:30
  • $\begingroup$ Under usual assumptions, the MSE is indeed unbiased. (stats.stackexchange.com/questions/111309/…) $\endgroup$ Mar 22 '19 at 14:46

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