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cov matrix of sample means, variances and covariances

• To: mathgroup at smc.vnet.net
• Subject: [mg15200] cov matrix of sample means, variances and covariances
• From: Albert Maydeu-Olivares <amaydeu at nil.fut.es>
• Date: Tue, 22 Dec 1998 04:01:33 -0500
• Sender: owner-wri-mathgroup at wolfram.com

Hi,

Does anyone know how to efficiently compute the covariance matrix of the
sample means, covariances, and variances of a subj x nvars data matrix?

I enclose a notebook with some code I wrote with a 300 x 4 matrix of
binary data. 
It's very slow. 

I would not like to use use it on a 1000 x 50 matrix!!



In[1]:=
T[matrix_List] := Transpose[matrix]
L[matrix_List] := Length[matrix]
Diag[matrix_List] := Table[If[i == j, matrix[[i,j]], 0], {i, L[matrix]},
{j, L[matrix]}]
VecLow[matrix_List] := Flatten[MapIndexed[Take[#1, First[#2] - 1] & ,
matrix]] VecLowDiag[matrix_List] := Flatten[MapIndexed[Take[#1,
First[#2]] & , matrix]] VecDiag[matrix_List] := Table[matrix[[i,i]],
{i, Length[matrix]}]

In[2]:=
patterns = {{0, 0, 1, 1}, {0, 1, 1, 1}, {1, 0, 0, 0}, {1, 0, 0, 1}, {1,
0, 1, 0}, {1, 0, 1, 1}, 
    {1, 1, 0, 0}, {1, 1, 0, 1}, {1, 1, 1, 0}, {1, 1, 1, 1}}//N;  obsfreq
= {39, 10, 30, 51, 24, 12, 19, 20, 43, 52}; n = L[obsfreq];  data =
Flatten[Table[Table[patterns[[i]], {obsfreq[[i]]}], {i, n}], 1]; subj =
L[data]; 

nvars = L[T[data]]; l = nvars + Binomial[nvars, 2]; 


Timing[dmat = Table[dd = {data[[i]]}; mat = T[dd] . dd; 
       dj = Flatten[{VecDiag[mat], VecLow[mat]}], {i, subj}]; 

       dmean = Table[Table[Sum[dmat[[i,j]], {i, subj}], {j, l}]/subj,
{k, subj}]; 
   
       w = T[dmat - dmean] . (dmat - dmean)/subj; ]

Out[2]=
{23.95 Second,Null}

N[w,3]//MatrixForm

----------------------------------------------------------------------------
Albert Maydeu-Olivares				Tel. +34 93 4021079 ext. 3099 Faculty of
Psychology 				Fax. +34 93 4021362 University of Barcelona				E-Mail:
amaydeu at tinet.fut.es Passeig de la Vall d'Hebron, 171.  
08035 - Barcelona (Spain)
----------------------------------------------------------------------------

• Follow-Ups:
  • Re: cov matrix of sample means, variances and covariances
    • From: Jurgen Tischer <jtischer@col2.telecom.com.co>