{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,27]],"date-time":"2025-02-27T05:31:29Z","timestamp":1740634289714,"version":"3.38.0"},"reference-count":49,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2010,10,18]],"date-time":"2010-10-18T00:00:00Z","timestamp":1287360000000},"content-version":"unspecified","delay-in-days":6713,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1992,6]]},"abstract":"<jats:p>A Sharpening Of Nonuniform bounds of the Berry-Esseen type initially obtained by Esseen and later generalized by Kolodja\u017eny\u012d\u2013who also proved that they are, in some sense, optimal\u2013is 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\u2013Esseen 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.<\/jats:p>","DOI":"10.1017\/s0266466600012779","type":"journal-article","created":{"date-parts":[[2010,10,18]],"date-time":"2010-10-18T09:12:04Z","timestamp":1287393124000},"page":"223-240","source":"Crossref","is-referenced-by-count":2,"title":["Improved Berry-Esseen-Chebyshev Bounds with Statisical Applications"],"prefix":"10.1017","volume":"8","author":[{"given":"Jean-Marie","family":"Dufour","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marc","family":"Hallin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2010,10,18]]},"reference":[{"key":"S0266466600012779_ref019","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176996280"},{"key":"S0266466600012779_ref017","first-page":"93","volume-title":"Asymptotic Statistics 2, Proceedings of the Third Prague Symposium on Asymptotic Statistics","author":"Helmers","year":"1984"},{"key":"S0266466600012779_ref011","doi-asserted-by":"publisher","DOI":"10.2307\/3314608"},{"key":"S0266466600012779_ref044","unstructured":"44. van Beek P. 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