Talk:Consistent estimator

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The closing claim jumps too quickly. What if $|\alpha _{n}|\to |\alpha |>1$ and ${\frac {\varepsilon }{\alpha }}<\varepsilon$? —Preceding unsigned comment added by 140.119.162.88 (talk • contribs) 22 January 22, 2008

related to other concepts

unbiased implies consistent?! the variance goes to zero as n->infinite, then it is consistent. Jackzhp (talk) 19:34, 19 April 2008 (UTC)

the variance doesn't necessarily go to zero as $n\rightarrow \infty$. But yes, many unbiased estimators are consistent. --Zvika (talk) 07:14, 20 April 2008 (UTC)

Tried to put this in, can someone check my reasoning. Lionfish0 (talk) 17:04, 20 January 2011 (UTC)

Can anyone give an example of an unbiased estimator that isn't consistent? I mean a real example of an estimator that might conceivably be used. I've never come across such an estimator. Obviously it's possible to concoct a totally artificial example. Qwfp (talk) 19:43, 20 January 2011 (UTC)

Well, for an iid sample {x
₁, x
_n} one can use T(X) = x
₁ as the estimator of the mean E[x]. This estimator is obviously unbiased, and obviously inconsistent.  // stpasha »  09:27, 21 January 2011 (UTC)

Thanks Stpasha, that's a nice simple example and probably worth putting in the article. Do you have a reference to ensure it isn't badged as WP:original research? I've never seen it used in practice, but I guess it's conceivable: the 'lazy estimator' that just uses the first piece of data to hand even when more are available. --Qwfp (talk) 09:56, 21 January 2011 (UTC)

That's frustrating! Can't we include an example though? For example, the 'standard deviation' page has an example in "Basic examples" that is technically original research, but is a useful illustration? Similarly, the 'Integration by Parts' has examples that aren't referenced). I hope my contribution wasn't original research too! I've put them both in, and crossed my fingers that they're just examples, and don't strictly need a reference (in the same way as examples on other pages don't need references). Thanks! Lionfish0 (talk) 14:44, 21 January 2011 (UTC)

Expanding content, example.

Tried to make this a little more readable. If anyone has current edition of Lehman handy, please update my page references.

Also, not sure that the "Properties" section as written really belongs here as written. IMO, Definitions, basic examples and statements of the most important results belong on wikipedia. Detailed technical proofs are perhaps best left to textbooks and other references. --Zaqrfv (talk) 13:37, 25 August 2008 (UTC)

Example of Unbiased Estimator that is not Consistent

The current example does not seem to be quite right. Just because an iid sample is chosen x(1) cannot be unbiased. I think a more specific example is required. Say an exponential distribution with parameter 1 since expectation of the estimator given here is 1. — Preceding unsigned comment added by Iamrohitbanga (talk • contribs) 05:08, 11 October 2011 (UTC)

Example for biased but consistent estimator

In the last example for biased but consistent estimator there is the term $-\theta /n$ missing: $E[T_{n}]=P(T_{n}=\theta )\theta +P(T_{n}=n\delta )n\delta =\theta -\theta /n+\delta$.