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Nonlinear regression with a complex-valued model function


Hi Everyone,

I have an application where I am trying to fit a trajectory in the
complex plane to a set of complex data points. The trajectory is
parameterised by several real parameters. I can find MLE values for
the parameters easily by least-squares, i.e. minimising the squares of
the distances between the data points and the matching points on the
trajectory, but I am uncertain about how to generate confidence
intervals for the parameters. These are usually calculated using
gradients of the model (trajectory) function, which is complex in this
case. Can anyone point me to a succinct generalisation of the linear
confidence interval theory to complex-valued model functions?

Thanks,
Mike Trefry  <mike.trefry at csiro.au>
CSIRO Land and Water
Australia


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