Talk:Cramér-Rao inequality
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[edit] Lower/Upper bound
"Upper bound" is correct in the first paragraph, where we speak of "accuracy". The Cramer-Rao inequality gives the maximum accuracy that can be achieved. Later, we speak about variance and there it is in fact a lower bound. High variance means low accuracy and vice versa.
This was changed recently, I have changed it back. -BB
- I didn't read carefully the first time, if we're talking about variance then the correct concept is precision not accuracy. Accuracy ties in with unbiasness. I feel we should not bring in accuracy or precision here since traditionally the CRLB is used in direct relation to the variance.
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- I like it as you have put it now, using precision instead of accuracy. The first sentence now expresses well the basic message of the CRB: It tells you how good any estimator can be, thus limiting the "goodness" by giving its maximum value. -BB
[edit] Too Technical
I have a science/engineering background, but can't begin to understand this. If I could suggest a change, I would. —BenFrantzDale
- Hi BenFranz. I'm happy to improve the article. What bit don't you understand? Robinh 14:32, 6 January 2006 (UTC)
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- For starters, a sentence or two on how this inequality is used (i.e., in what field does it come up) would be helpful. I don't know how specialized this topic is, but I like to think I have most of the background needed to get a rough understanding of it. A list of prerequisites, as described on Wikipedia:Make technical articles accessible would be helpful. —BenFrantzDale 16:25, 6 January 2006 (UTC)
It's used where statistical estimation is used. Read the article on Fisher information. Michael Hardy 22:54, 9 January 2006 (UTC)
[edit] a correction for the example for the cramer-rao ineqality
My name is Roey and I am a student in my third year for industrial engineering in T.A.U, I have a correction for the example given here for cramer rao inequality: the normal distibution formula is incorrect and for some reason I can`t insert it here, in the example the formula has not divided the (x-m)^2 by 2*teta, instead, it is devided by teta. thus the final result is incorrect. The right result should be: 1/2*teta^2 (and not 3 times this number) I have continued this example correctly by I can`t get it to here.... Have a good day and tell me how can I put the correct answer here please...
Roey
[edit] Error in Example
As Roey I found that the example for the Gaussian case was mistaken. I have corrected it. Indeed this example achieves the CR bound. Anyway I'm not too much familiar with this math. I would acknowledge if the original author or other reader will confirm the change.
Viroslav
[edit] what log means
Hi, shouldn't what log means here be defined, or better yet Ln is used instead of log?
MrKeuner
[edit] more example suggestions
Pursuant to the example, it's common to think of the information as the variance of the score (by definition) or the negative expectation of the second derivative of the log likelihood (when it exists); it threw me for a minute to think of the information as the negative expectation of the derivative of the score. In my experience, one generally choses one or the other representation and not a mix of both.
What "log" means for likelihood problems is generally not an issue, (it should be natural log to negate the antilog in the gaussian example) but the standard book notation uses plain "log" with the understanding that it means natural log.
