Readme file
SERIES
B
 Statistical
Methodology
The complex Bingham quartic distribution and shape analysis,
Journal of the Royal Statistical Society, Series B, volume
68 (2006), part 5, pages 747 - 765
The files comprise the following:
fb5ml.data -- Whin Sill data;
qcet2.data -- mouse vertebrae data;
cbq9.r -- R routines to carry out cbq analysis;
example.r -- sample file of commands to reproduce output of
the paper.
The R routines have not been packaged as a library, but are in the file
cbq9.r
The routines are not very polished and may need refining for awkward datasets,
but here is a brief description of how to use them.
1. Read in the R routines using
source("cbq9.r")
2. The data should be presented in the form of a complex n x p matrix,
zh, say where each row is a unit vector.
3. Carry out some preliminary calculations by setting
pre=preliminaries(zh)
4. Set nparam=1,2, or 3 depending on whether you wish to estimate all
the parameters, just the concentration parameters, or just the
mean parameters (with any parameters not being estimated fixed
at the tangent estimator values).
5. Do some preparations for the saddlepoint aprrox by
prep=cbq.sadint5.prep(pre$Omega0.half%*%pre$Omega0.half,niter=1)
6. Set con.ind=1,2,3 or 4 depending on which approximation to the normalizing
constant is to be used (simple asymptotic, refined asymptotic, saddlepoint
or exact (the last only available if p=2). Then run
param=pre$param0; p=pre$p; p2=2*p-2
if(nparam==2) param=param[1:(p2*(p2+1)/2)]
if(nparam==3) param=param[(p2*(p2+1)/2)+(1:p2)]
out=nlm.vm(cbq.mlden8.std,param,pre=pre,prep=prep,constr=constr.cbq.std,
con.ind=con.ind, nparam=nparam,niter=1,verbose=0)
7. Then "out" contains various pieces of information about the
fitted parameters. To get the parameter estimates in the mean-standardized
coordinate", run
process(zh,pre=pre,out)
8. The parameters can be mapped back to the original coordinates using
pre$g0 which corresponds to the complex conjugate of G(mu) in the paper.
9. Some further information about comparing parameter estimates can be
found in the file example.r
J. T. Kent
Department of Statistics
University of Leeds
Leeds
LS2 9JT
UK
E-mail: J.T.Kent@leeds.ac.uk
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