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Calculating Covariance Matrix

• To: mathgroup at smc.vnet.net
• Subject: [mg30227] Calculating Covariance Matrix
• From: "Mark Coleman" <mcoleman at bondspace.com>
• Date: Fri, 3 Aug 2001 00:55:58 -0400 (EDT)
• Organization: BondSpace, Inc.
• Sender: owner-wri-mathgroup at wolfram.com

Greetings,

Here is a problem for you Mathematica list-wizards. I am working with a data set 
that, for a number of reasons is best organized as a long list of (mxn) 
matrices (each matrix can be thought of as a transition matrix (with 
some absorbing states, so that m <> n). I would like to calculate a 
vairety of sample statistics, the mean, median, covariance, etc. for 
this data. The statistics should be calculated by by working 'across' 
each element of each matrix in the list. That is, the mean will be an 
nxm matrix where element [[i]][[j]] of the mean matrix is the mean of 
the [[i]][[j]] elements of the matrix in the list. For the mean, the 
usual Mathematica procedure works just fine: 

Apply[Plus,dataList]/Length[dataList]

But the organization of the data precludes the use of the procedures in 
the Statistcs`DescriptveStatistics add-on. I would be especially 
interested in someone could show me a way of calculating the covariance 
and median of my list using list operators directly. Is there a way of 
doing the calculations without breaking the list or re-organizing it?

Thanks,

-Mark