What is a good distance function to compare covariance matrices of different sizes?

Question

Is there by any chance something analogous to a ratio test, but for covariance matrices instead of variances? I know how to use the F-test for variances, but I would like to compare covariance matrices to see what I can learn about goodness of fit for nonlinear regression, looking at fits using different numbers of parameters (in this case, summing different numbers of exponentials to get my fit function).

Answer 1

its not a distance function you need but the distribution of the distance function. Recall that the likelihood Ratio test works because we know in certain cases the distribution of the ratio. There are a wide range of measures one can use to assess the fit of non-linear models. I am not sure what non-linear model you are using but for a number of common linear model r squared measures have been worked out along with adjustments for the number of model parameters. Sorry if this doesn't entirely answer your question.

Answer 2

a2 +b2= c2
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