Talk:Cramér–Rao bound

message: For the scalar unbiased case two definitions are given, namely:
:
I(\theta) = n \operatorname{E}
 \left[
  \left(
   \frac{\partial \ell(x;\theta)}{\partial\theta}
  \right)^2
 \right] = -n \operatorname{E}\left[ \frac{\partial^2 \ell(x;\theta)}{\partial\theta^2} \right]
Now, according to the page on Fisher information the second definition (the one with the second derivative) only holds when certain regularity conditions are met. I think it should be mentioned on this page too, so I added it. I came by this by calculating CRB for my own estimator for which the regularity conditions do not hold and ended up with a negative fisher information.  — Preceding unsigned comment added by Scloudt (talk • contribs) 12:28, 24 May 2020 (UTC)
replies: text: Stupid question: The n strikes me as unintroduced in this article, and also not correct. Where does it come from, or am I missing something? Marcusmueller ettus (talk) 08:43, 20 January 2023 (UTC)
thread_title: Alternative expression for CRLB

message: My understanding is that CRLB exists for biased estimators too. However it is considerably simpler in the unbiased case where the form of the bound does not depend upon the estimator used (it's the same for all unbiased estimators). Might it not be worth stating this somewhere so as not give give the impression that CRLB ONLY exists for unbiased estimators?
MB
86.144.38.235 15:15, 11 April 2007 (UTC)
replies: text: Sounds like a good idea, go ahead and be bold! --Zvika 12:40, 12 April 2007 (UTC)
thread_title:  Cramer Rao lower bound is not just for unbiassed estimators 

message: I've made some significant changes to the article. I hope you like them. The main difference is that I changed the order so that the statement of the bound, in its various forms, appears before examples and proofs. This seems to me the correct order for an encyclopedia. I also added a version of the bound for biased estimators, as requested by User:86.144.38.235. Finally, I tried to simplify the mathematical expressions a little bit, especially in the vector case. --Zvika 17:32, 19 May 2007 (UTC)
thread_title:  Some major changes 

message: I find the redirect from Information inequality a bit misleading; I was looking for Inequalities in information theory... - Saibod (talk) 17:37, 20 October 2011 (UTC)
replies: text: I have replaced the redirect by a disambig page. However, note that presently no articles use a wikilink to Information inequality. Melcombe (talk) 08:47, 21 October 2011 (UTC)
replies: text:  Thanks! I didn't feel "bold" enough to do it myself, so it encourages me to see that someone did it. Is it a problem that no articles use a wikilink to information inequality? - Saibod (talk) 08:46, 26 October 2011 (UTC)
replies: text: Not particularly, as it provides a route in for anyone searching for the term "information inequality". But it may be worth checking articles for the phrase ""information inequality" to see if there needs to be a wikilink either to one of the aticles or to the disambig page. Melcombe (talk) 08:53, 27 October 2011 (UTC)
thread_title:  redirect from [[Information inequality]] 

message: θ  — Preceding unsigned comment added by Ttenraba (talk • contribs) 12:28, 29 May 2017 (UTC)
thread_title:  Definition of function ψ(θ) is confusing.  

message: Hello fellow Wikipedians,
I have just modified one external link on Cramér–Rao bound. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
*Added archive https://archive.is/20121215055105/http://www4.utsouthwestern.edu/wardlab/fandplimittool.asp to http://www4.utsouthwestern.edu/wardlab/fandplimittool.asp
When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
Cheers.—InternetArchiveBot (Report bug) 04:26, 14 August 2017 (UTC)
thread_title:  External links modified 

message: In the general scalar case, in my opinion, it is not a matter of T being a biased estimator of \theta, but being an unbiased estimator of \psi(\theta). Madyno (talk) 12:14, 18 February 2021 (UTC)
thread_title:  General scalar case  

message: https://link.springer.com/article/10.1007/s11760-019-01571-9 Generalized Cramér–Rao inequality and uncertainty relation for fisher information on Fractional Fourier Transform
(2019) Biggerj1 (talk) 21:25, 25 May 2023 (UTC)
thread_title:  Very interesting connection to the [[uncertainty principle]] and Fourier transform  

message: Can somebody find a source for the equations on this website? https://theoryandpractice.org/stats-ds-book/statistics/cramer-rao-bound.html if the formula is correct, it would be worth adding it to the article Biggerj1 (talk) 07:00, 8 June 2023 (UTC)
thread_title:  Biased estimators