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.
"Bounds on the Rate of Convergence of Moments in the Central Limit Theorem." Ann. Probab. 10 (4) 1004 - 1018, November, 1982. https://doi.org/10.1214/aop/1176993721