posts tagged * Glivenko-Cantelli theorem

In search of the fundamental theorem of statistics: arriving at (Bernoulli 1713)


Many mathematical disciplines call one result their fundamental theorem. Recall the fundamental theorem of algebra or the fundamental theorem of calculus. There are many more theorems named “fundamental theorems” for subdisciplines as exotic as, for example, ideal theory in number fields. What is missing, though, is something people agreed upon calling the “fundamental theorem of statistics”. Here, I will discuss a few candidates for this title, including the central limit theorem as well Bayes’ theorem, and finally argue that most promising is a historic precursor of the law of large numbers sometimes called “Bernoulli’s theorem”.

read more