Talk:Bias of an estimator

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Contents 1 Work needed on 'Estimating a Poisson probability' example 2 Bayesian critique ? 3 unbiased ? 4 two problems

[edit] Work needed on 'Estimating a Poisson probability' example

I was looking over this article, and the section on estimating a Poisson probability appears quite messy and disjointed. I do not currently have the time to clean this up, but I wanted to bring it to others' attention. Wolf87 23:53, 11 February 2007 (UTC)

The only thing that I immediately notice that needs improvement in that section is that it's a bit silly to make an issue of mean squared error being large after a far more damaging case against unbiasedness (in this case) has been presented. So I wonder if you can be more specific? Michael Hardy 00:57, 12 February 2007 (UTC)

[edit] Bayesian critique ?

Should this article include a Bayesian critique of unbiasedness ?

If I understand it correctly, the test for an unbiased estimator is that

But that is quite a different thing from being able to say that

Of course for frequentists the latter proposition is difficult, because to evaluate it requires the specification of a prior probability for θ.

But, for example, in some stuff I'm working through at the moment there's a case where an unbiased estimator is known and widely trumpeted as such; but where on every reasonable prior for the system, including a uniform prior and a Jeffreys' prior, the so-called unbiased estimator is guaranteed to estimate low of the mean, every time.

And yet people treat unbiasedness as a fetish, or a wonderful comfort blanket. The word 'unbiased' is repeated again and again in the literature I'm reading for the problem. The word seems to block any understanding of the systematic error that an 'unbiased' estimator can lead to. Jheald 19:39, 26 February 2007 (UTC)

[edit] unbiased ?

An estimator or decision rule having nonzero bias is said to be biased. Should the second sentecein the first paragraph read 'unbiased' rather than 'bisaed'?

No. If the bias is nonzero, then it's biased. If the bias is zero then it's unbiased. Michael Hardy 21:59, 11 June 2007 (UTC)

[edit] two problems

1. The variance of a population given in the examples section is only correct for a uniformly distributed population.

2. The same example section suggests that the biased estimator of the variance is "more useful" than the unbiased estimator merely because we divide by a bigger number. This seems absurd. Am I missing something? 98.224.223.201 (talk) 00:03, 27 January 2008 (UTC)