# Talk:Minimum-variance unbiased estimator

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Michael Hardy wrote:

Deleting nonsense. I already deleted this assertion before; whether from this article or a closely related one I don't know. Is someone teaching this crap in some signal-processing course?

regarding [1]. Seriously, what's the problem here?

The MVUE is equivalent to the minimum mean squared error (MMSE) since the bias is constrained to zero.
In other words, if the bias is zero then the MMSE is the MVUE (if it exists).

If the estimator is unbiased then minimizing the variance is the same as minimizing the MSE, so it's both the MVUE and MMSE. Where exactly is the "crap" here? Cburnett 01:00, 10 Mar 2005 (UTC)

IF and estimator is unbiased.
Read the line above! That's far too big an "if"! Your assertion seems to be saying that the minimum-variance unbiased estimator has the smallest MSE of ANY estimator, since it has the smallest MSE of any UNBIASED estimator. In other words, you seem to be assuming that the estimator with the smallest MSE can only be an unbiased estimator.
Your words above make me suspect that you meant something else: you might have meant it has the smallest MSE of all unbiased estimators, rather than the smallest MSE of all estimators. If that's what you meant, then your meaning was completely unclear. Let's look at what you wrote:
The MVUE is equivalent to the minimum mean squared error (MMSE) since the bias is constrained to zero. In other words, if the bias is zero then the MMSE is the MVUE (if it exists).
Combining what I deleted from the article, immediately above, with your words on this discussion page, it does look as if that other meaning is what you had in mind. Apparently by "MMSE" you meant NOT "minimum mean squared error estimator" but rather "minimum mean square error unbiased estimator". If that's what you meant, then what you meant was right. But it's hard to tell that that's what you meant, given what you wrote, since when you wrote "minimum mean square error" you didn't wrote "mimumum mean squared error UNBIASED estimator".
In some cases, there are biased estimators that have far smaller mean squared error than the MSE of the best unbiased estimator. Michael Hardy 01:34, 10 Mar 2005 (UTC)
Yes, "you might have meant it has the smallest MSE of all unbiased estimators, rather than the smallest MSE of all estimators" is true and I have no problem admitting it was unclear, so can we cooperate to get something clear put into the article or do we have to keep dodging that and I can keep setting you up for more "teaching this crap in some signal-processing course" type of comments? Cburnett 05:28, 10 Mar 2005 (UTC)

## Hand-holdy

I started with this:

While the particular specification of "optimal" here — requiring unbiasedness and measuring "goodness" using the variance — may not always be what is wanted for any given practical situation, it is one where useful and generally applicable results can be found.

which struck me as too hand-holdy for an encyclopedia.

Then, trying to maintain the original spirit, I wound up with this:

While combining the constraint of unbiasedness with the desirability metric of least variance leads to good results in most practical settings—making MVUE a natural starting point for a broad range of analyses—a targeted specification may perform better for a given problem; thus, MVUE is not always the best stopping point.

I can't say I'm loving that, either, although it does conform to the standard template of advice I've received many times from various machine learning podcasts: do this simple, deeply-motivated thing first, and only then, if you're sure you need to, try the special blades.

Perhaps the real solution here is simply better material. — MaxEnt 20:45, 7 May 2017 (UTC)