I have read the article by Vapnik, Chervonenkis "On the uniform convergence of relative frequencies of events to their probabilities" Theory of Probability and Its Applications, vol XVI, n. , 1971.

There it is explained the theory of convergence of the relative frequencies computed in a histogram -- correct?

My question is a practical one: How could I test whether the histogram I have computed has actually converged to the underlying density distribution? Moreover, does Vapnik, Chervonenkis theory tell us something in how to shape my histogram ? in other words, is it better to have equal frequencies bins or equal lenght bins?

Finally, what does Vapnik, Chervonenkis theory suggest us about sample size?

In conclusion, I have read the Vapnik, Chervonenkis reference but I need a more explicative texbook or simply some hints to apply it plainly.

PS: a curiosity, but what is the difference between Vapnik, Chervonenkis contribution in 1971 and the Glivenko Cantelli theorem?


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