A New Direct Proof of the Central Limit Theorem

Vladimir Dobric; Patricia Garmirian

A New Direct Proof of the Central Limit Theorem

Probability 2015-10-29 v2

Authors: Vladimir Dobric , Patricia Garmirian

Abstract

We prove the Central Limit Theorem (CLT) from the definition of weak convergence using the Haar wavelet basis, calculus, and elementary probability. The use of the Haar basis pinpoints the role of $L^{2}([0,1])$ in the CLT as well as the assumption of finite variance. We estimate the rate of convergence and prove strong convergence away from the tails.

Keywords

central limit theorem weak convergence fundamental theorem

Cite

@article{arxiv.1507.00357,
  title  = {A New Direct Proof of the Central Limit Theorem},
  author = {Vladimir Dobric and Patricia Garmirian},
  journal= {arXiv preprint arXiv:1507.00357},
  year   = {2015}
}

Comments

12 pages

Related papers

View all related →