Next: Goodness-of-fit tests
Up: MAXIMUM LIKELIHOOD METHODS
Previous: The estimation of the
All theory of the previous sections is based on the probability
of the distance between two points in phase space, which
depends on the correlation dimension or .
By taking the maximum of distances between -couples of
points [Ellner, 1988,Grassberger and Procaccia, 1984], the for integer values of
can be estimated,
but this requires a much larger number of points.
It could be that the method of generalizing the correlation
integral as described in Chapter 4 can be used to derive
maximum likelihood estimators of .
Furthermore, Göttsche and Huber [Göttsche and Huber, ] estimate
the spectrum of singularities [Halsey et al., 1986],
from which the can be computed.