ABSTRACT
In this section, we present the basic Central Limit Theorem for i.i.d. variables. We do this for vector variables since the proof is essentially the same as for one-dimensional variables. The extension to independent nonidentically distributed random variables, due to Lindeberg and Feller, is stated without proof. Applications are given to some important statistical problems: to least-squares estimators of regression coefficients, to randomization tests for paired comparison experiments, and to the signed-rank test.
