Salsburg, D. 2001.
``
The Lady Tasting Tea
-- How statistics revolutionized science
in the twentieth century''.
Owl Book.
Chapter 28.
The computer turns upon itself
The Glivenko-Cantelli lemma is one of those results that
appears to be intuitively obvious, but only after it was discovered. If
nothing is known about the underlying probability distribution that
generated a set of data, the data themselves can be used to construct
a nonparametric distribution. This is an ugly mathematical functions,
filled with discontinuous and lacking in any kind of elegance.
But in spite of its awkward structure, Cantelli was able to
show that this ugly empirical distribution function got closer and
closer to the true distribution function as the number of observations
increased.