Talk:Estimation of covariance matrices

From Wikipedia, the free encyclopedia

You have new messages (last change).

[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 elements 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)

Retrieved from "http://en.wikipedia.org../../../e/s/t/Talk%7EEstimation_of_covariance_matrices_0fc9.html"