EconPapers    
Economics at your fingertips  
 

Improved Berry-Esseen-Chebyshev Bounds with Statisical Applications

Jean-Marie Dufour () and Marc Hallin ()

Econometric Theory, 1992, vol. 8, issue 02, 223-240

Abstract: A Sharpening Of Nonuniform bounds of the Berry-Esseen type initially obtained by Esseen and later generalized by Kolodjažnyĭ–who also proved that they are, in some sense, optimal–is proposed. Further, the corresponding inequalities are shown to provide uniformly improved Chebyshev bounds for the tail probabilities of the distribution functions to be approximated. In contrast with most results on Berry–Esseen bounds, which emphasize rates of convergence to normality, the bounds proposed are sufficiently explicit to allow the computation of numerical bounds on a distribution function. For example, they can be applied to the sum of a small number of independent random variables. The bounds are easy to compute and can be used in confidence estimation as well as in testing problems. Applications include signed-rank tests, permutation tests, and the chi-square approximation to Bartlett's test statistic for the homogeneity of several variances.

Date: 1992
References: Add references at CitEc
Citations: Track citations by RSS feed

Downloads: (external link)
https://journals.cambridge.org/abstract_S0266466600012779 link to article abstract page (text/html)

Related works:
Working Paper: Improved Berry-Esséen-Chebyshev bounds with statistical applications (1992)
Working Paper: Improved Berry-Esseen-Chebyshev Bounds with Statistical Applications (1989)
Working Paper: IMPROVED BERRY-ESSEEN-CHEBYSHEV BOUNDS WITH STATISTICAL APPLICATIONS (1989)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cup:etheor:v:8:y:1992:i:02:p:223-240_01

Access Statistics for this article

More articles in Econometric Theory from Cambridge University Press Cambridge University Press, UPH, Shaftesbury Road, Cambridge CB2 8BS UK.
Bibliographic data for series maintained by Keith Waters ().

 
Page updated 2019-06-19
Handle: RePEc:cup:etheor:v:8:y:1992:i:02:p:223-240_01