A strengthened central limit theorem for smooth densities. (English) Zbl 0822.60018

The paper presents various local limit theorems for i.i.d. random variables with zero mean and positive (but finite) variance. The authors employ two different setups. One is based on a generalization of Fisher’s information and the other uses Fourier transformation. The results give convergence in various norms depending on the properties of the theoretical density.
Reviewer: P.Lachout (Praha)


60F05 Central limit and other weak theorems
62E20 Asymptotic distribution theory in statistics
Full Text: DOI