For some time now I have been struggling to understand how theoretical results can be applied in practice. Fortunately in most cases the link between theory and practice is not hard to find, for instance:
- You can directly use a theoretical result for your calculations.
- You cannot actually find a solution, but you at least have an upper or lower bound that can indicate how good your real solution is.
- By observing the theoretical formulas you can make something 'similar' and hopefully with similar performance
- The general case is only theoretical, but in special cases it can be applied directly.
Well, this is not everything, but I won't try to make a complete list of how statistical theory can be useful. Until now I have always succeeded in at least grasping the idea of how theory can be applied in practice.
However, it now appears that I have stumbled opon something of which I cannot see how it could possibly be applied.
I was studying some smoothing methods, amongst which (nonparametric) kernel smoothing, as described on Wikipedia , and found that there is a theoretical solution for the
AMISE, as well as the bandwidth,
hAMISE that optimizes it. However, both in the notes that I was reading, as well as the Wikipedia page I have been unable to find any practical application of this.
Is there any practical application for the
AMISE and its optimal bandwidth?
Discovering that there actually is an application for would be very motivating so I hope it can be achieved!