Introduction The cross validation is a common technique to calibrate the binwidth histogram. They are the simplest and, sometimes, the most effective tool to describe the density of some dataset.

The other day I was bounding some inequalities for my thesis. I had that some functions were Holder, but I haven’t the explicit derivatives of my functions. I spent one hour or so thinking if I could bound correctly my expression without having the derivatives. The answer is yes, and I will show how. Hölder …