Abstract:
Although it is difficult to believe that there may be something new to say about normal approximation in the twenty-first century, the fact still remains that there exists no simple and certain method of proving central limit theorems. All techniques known to statisticians and probabilists require extensive information about the nature of the system, and some good luck. On the other hand, variance bounds (and hence weak laws) are routine issues which daunt no one. The purpose of this talk is to introduce a new method by which it is possible to reduce every normal approximation problem to a variance bounding exercise. Applications, including one involving a nontrivial statistical problem (due to Peter Bickel), will be described.