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The berry-esseen inequalities derived from restricted convergence
Author:
Hans-Joachim Rossberg a
| Affiliation: | a Karl-Marx-University, Leipzig |
DOI:
10.1080/02331888908802194
Publication Frequency:
6 issues per year
Subjects:
Mathematical Statistics;
Statistical Theory & Methods;
Statistics;
Statistics for the Biological Sciences;
Stochastic Models & Processes;
Formats available:
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(English)
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Abstract
Let X1, X2, … be i.i.d.r.v. and write (X1+…Xn-An)/Bn~Fn, where Bn >0.AnER1, n≥1. It is known that solely one-sided asymptotic assumptions imposed on Fn imply Fn0. In the present note we show that stronger one-sided assumptions lead even to the existence of EX13 so that the BERRY-ESSEEN inequalities hold true.
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| Keywords: Primary 60F05; secondary 60E15; BERRY-ESSEEN inequality; restricted convergence |
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