Talk:Estimation of covariance matrices

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[edit] Biased vs. Unbiased estimate

Shouldnt we also note that the MLE is biased, and include a section on an unbiased estimator?

Perhaps, but I don't see any urgency about it. Most reasonable estimators, including most MLEs, are biased. Michael Hardy 22:00, 2 May 2005 (UTC)

Michael, please see if my piece fits well enough. -- Stas Kolenikov

Guys, please at least put some links for unbiased discussions. I got some strange phenomenon when I was doing a project, so I adjust the diagonal eleme nts to unbiased variance estimates. It seems work better. Jackzhp 12:48, 21 October 2006 (UTC)

[edit] notation

I'd like to point out that the symbol Σ starts out denoting a parameter, but then is later used as an estimator. Btyner 19:40, 9 February 2007 (UTC)

[edit] New summary and further proposed changes

I have rewritten the summary, putting the maximum likelihood estimator in perspective.

The use X and x should be made consistent throughout the article.

I am not sure about the purpose of the statement

Although no one is surprised that the estimator of the population covariance matrix is [closely related to] the sample covariance matrix, the mathematical derivation is perhaps not widely known and is surprisingly subtle and elegant.

for the following reasons:

  • The form with 1/n is not what is commonly called sample covariance matrix. For now I have added the text "closely related to" but that weakens the surprise part.
  • Subtlety, elegance, and surprise are subjective, and the information contents of the statement is zero.
  • The argument is nice but not all that subtle and elegant for that to be notable. (In my opinion, see the note above about subjective.)

Jmath666 14:34, 25 March 2007 (UTC)

I have now removed the statement above as proposed. Jmath666 23:05, 31 March 2007 (UTC)


[edit] linking to the article on "degrees of freedom"

In the beginning of the article, where we explaining way we divide by the factor n-1 rather than with n (in the unbiased estimator for the cov matrix), it is said that the reason is because the mean is not known and is replaced by the sample mean. Of course this is true. And more then that, it directs us to the notion of degrees of freedom. and thus should link to the article on Degrees of freedom (statistics). What do you think ? Talgalili 13:04, 25 August 2007 (UTC)