Talk:Covariance

message: For variance, there is a biased estimation,and an unbiased estimation. Is there any unbiased estimation for covariance? Jackzhp 17:55, 2 February 2007 (UTC)
replies: text: Yes. See sample covariance matrix. Prax54 (talk) 19:33, 10 August 2012 (UTC)
thread_title:  unbiased estimation 

message: It is customary to use \sigmaXY to represent covariance(x,y) and \sigma2 to represent variance.  Contrary to the above author's opinion that use of symbols adds nothing to the article, I believe that adding customary symbol usage will help people coming to this page while viewing material containing those symbols.Tedtoal (talk) 22:38, 12 March 2011 (UTC)
thread_title:  Add <math>\sigma</math>? 

message: Hello, I don't think this page is all that great for the lay person; as a matter of fact, I think the Definition section over-complicates things.  Wolfram MathWorld has us beat here: http://mathworld.wolfram.com/Covariance.html.  Anyone object to me incorporating this information into this page?  I'm particularly looking for feedback from folks who are significantly more stats-minded than myself. :)  Thanks, dmnapolitano (talk) 18:17, 27 September 2011 (UTC)
replies: text: Anyway: the present definition in math world many seem simpler, but is not correct. Nijdam (talk) 10:28, 9 June 2012 (UTC)
thread_title:  A simpler definition exists 

message: The article states the last formula may cause catastrophic cancellation if used in computing, but the first formula clearly can't be computed directly in that form.   So what equation should we use? 24.38.10.6 (talk) 14:34, 29 May 2013 (UTC)
thread_title:  Better Formula? 

message: The following was in the section "Properties", is it correct? (if so - we can add it again)
For sequences x1, ..., xn and y1, ..., ym of random variables, we have
: \sigma\left(\sum_{i=1}^n {x_i}, \sum_{j=1}^m{y_j}\right) =    \sum_{i=1}^n{\sum_{j=1}^m{\sigma\left(x_i, y_j\right)}}.\,
Tal Galili (talk) 06:39, 29 September 2013 (UTC)
thread_title:  IS this correct? 

message: I added the Hoeffding Covariance Identity to the article. I was not able to find a proof online though, how should I reference the result in this case?  — Preceding unsigned comment added by 46.227.2.125 (talk) 16:47, 2 August 2016 (UTC)
thread_title:  Hoeffding Covariance Identity 

message: I wonder why there is no link (at the very least) to covariance in physics, e.g. general covariance in relativity.  — Preceding unsigned comment added by 42.111.162.152 (talk) 02:47, 10 July 2019 (UTC)
replies: text: This article is not about the same definition of covariance. The "about" template at the beginning states,  The Covariance (disambiguation) page links to several articles which mention covariance in mathematics and physics.—Anita5192 (talk) 04:44, 10 July 2019 (UTC)
thread_title:  No reference to physics??? 

message: Under the heading "Definition", COV(X,Y) = E[(X-E[X])(Y-E[Y])] = E[XY] - E[X]E[Y]
Under the heading "Discrete random variables", COV(X,Y) = SUM( i=1:n; P_i*(x_i-E[X])*(y_i*E[Y]) ); I'll refer to this definition below as COV1. For discrete r.v's, this is the same as the defn in terms of expected value. All good.
Under the heading "Example", COV(X,Y) = SigmaXY = SUM( (x,y) elementof S; f(x,y)*(x-MuX)*(y-MuY) ); I'll refer to this sum as COV2.
My understanding is that COV2 can be written as COV2(X,Y) = SUM( j=1:n; SUM( k=1:m; f(x_j, y_k)*(x_j-MuX)*(y_k-MuY) ) ); this is how the example calculates the COV from the table.
It would be helpful if the article could clear up how COV1 is equivalent to COV2 (I've not been able to nor can I see how to do so).
This ambiguity is widespread (and is not confined solely to this article); any number of stats books interchangeably use COV1 and COV2 to calculate the correlation coefficient, often using both within a breath of each other. 
Dig a bit more and the defn of expected value is ambiguous.  Is it (a) E[X] = SUM( j=1:n; x_j*f(x_j) ) OR is it (as given for joint distns) (b) E[XY] = SUM( j=1:n; SUM( k=1:m; f(x_j, y_k)*x_j*y_k ) )? Does E[XY] (a) equal E[XY] (b) ?
There's surely a gap in my stats knowledge but shouldn't these books and articles like this fill this gap ?
Thanks. DP3285 (talk) 04:28, 6 November 2022 (UTC)
thread_title:  COV definition & example use are different (aren't they?)