Example
As an example, consider empirical distribution functions. For real-valued iid random variables they are given by
In this case, empirical processes are indexed by a class It has been shown that is a Donsker class, in particular,
- converges weakly in to a Brownian bridge B(F(x)) .
Read more about this topic: Empirical Process
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“Our intellect is not the most subtle, the most powerful, the most appropriate, instrument for revealing the truth. It is life that, little by little, example by example, permits us to see that what is most important to our heart, or to our mind, is learned not by reasoning but through other agencies. Then it is that the intellect, observing their superiority, abdicates its control to them upon reasoned grounds and agrees to become their collaborator and lackey.”
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