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A Berry-Esseen Bound for Linear Combinations of Order Statistics
Authors:
Gyula Pap a;
Martien C. A. Van zuijlen b
| Affiliations: | a Lajos Kossuth University, Hungary |
| b University of Nijmegen, The Netherlands |
DOI:
10.1080/02331889808802633
Publication Frequency:
6 issues per year
Subjects:
Mathematical Statistics;
Statistical Theory & Methods;
Statistics;
Statistics for the Biological Sciences;
Stochastic Models & Processes;
Formats available:
PDF
(English)
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Abstract
The rate of convergence of the distribution function of a linear combination
 of order statistics of n independent and identically distributed random variables with a common distribution function F to its normal limit is investigated. Under the assumptions
  some  1,  , 2, β2 > 0 and
 with some 0 ≤ κ < 4/3 and appropriate moment conditions a Berry-Esseen bound is given. If the coefficients are generated by a sequence of weight functions of a special structure, then the rate is shown to be  . Finally, the result is applied for a statistic, which is widely used in auditing.
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| Keywords: Linear combinations of order statistics; Berry-Esseen bound; Stringer bound |
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