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What is the validity of using a kernel density estimation to compare model x observed data?

In other words, if the KDE curve for the observed data looks like the KDE for the model forecast, can I use this result as a quality measure for the model? If not, why?

In this case, it's a weather forecast model - but I have some complex variables like wind direction, for which a simple correlation will not help too much. For example, the wind going from 360 to 5 is a huge numeric decrease, but it's almost the same direction!

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I don't think you can do that. Suppose you have a vector of data [-1,0,1] and your model predicts [1,-1,0]. That has the same histogram, but you are off on all points. A marginal predictive improvement of [1,0,-1], where you get the 2nd observation correct, also has the same distribution.

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  • $\begingroup$ Yes, i thought about that. But besides this, is there something useful i can take from the KDE's? $\endgroup$ – Fernando Oct 3 '13 at 0:42
  • $\begingroup$ I think the differences in KDEs can be useful. I often have data with a big spike at zero and if I don't see that in the model output, I know I am in trouble. Often I like to create bins and make a confusion matrix. If I say the wind was blowing NW, how often did I get it right and if I got it wrong, how? For your wind example, there might be some useful transformation that makes correlation-type measures or confusion matrices more interpretable. Maybe vector mean direction? Perhaps that would make a nice separate question. $\endgroup$ – Dimitriy V. Masterov Oct 3 '13 at 1:05
  • $\begingroup$ Here's an example of circular correlation coefficient. $\endgroup$ – Dimitriy V. Masterov Oct 3 '13 at 1:10
  • $\begingroup$ That's exactly what i'm using by now - the accuracy rate from the 8x8 confusion matrix (1 division at each 45 degree). Thanks for your insights, definitely going to check your refs, and maybe post a separate question later. $\endgroup$ – Fernando Oct 3 '13 at 1:15
  • $\begingroup$ Another good reference is Fisher, N.I. 1993. Statistical Analysis of Circular Data. Cambridge: Cambridge University Press. $\endgroup$ – Dimitriy V. Masterov Oct 3 '13 at 1:20

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