Bounds on the Rate of Convergence of Moments in the Central Limit Theorem

Abstract

We derive two-sided bounds on the rate of convergence of moments in the central limit theorem. A variety of norming constants is considered, and it is shown that a very delicate alteration to these constants can have a significant effect on the rate. Indeed, the influence of norming constants on rates of convergence of moments is of a more subtle nature than in the central limit theorem itself. We present several examples to illustrate some extreme cases.