       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

```

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