A Berry-Esseen Bound for Linear Combinations of Order Statistics

References

• Anderson , R. J. and Teitlebaum , A. D. 1973 . “ Dollar-unit sampling ” . In Canad. Chartered Accountant 30 – 3 . (after 1973, this publication became CA Magazine)
   Google Scholar
• Bentkus , V. , Götze , F. and Tikhomirov , A. 1997 . Berry-Esseen bound for statistics of weakly dependent samples . Bernoulli , 3 : 329 – 350 .
   Google Scholar
• Bentkus , V. , Götze , F. and van Zwet , W. R. 1994 . An Edgeworth expansion for symmetric statistics . Ann. Statistics , 25 : 851 – 89 . Preprint No. 94–020 Sonderforschungsbereich 343, Diskrete Strukturen in der Mathematik, Bielefeld.
   Google Scholar
• Bickel , P. J. 1992 . Inference and auditing: the Stringer bound . International Statistical Review , 60 : 197 – 20 .
   Web of Science ®Google Scholar
• Bjerve , S. 1977 . Error bounds for linear combinations of order statistics . Ann. Statist. , 5 : 357 – 36 .
   Google Scholar
• David , H. A. 1981 . “ Order Statistics ” . New York : John Wiley and Sons .
   Google Scholar
• Friedrich , K. O. 1985 . “ Dissertation ” . In Berry-Esseen Abschätzungen für Nichtparametrische Statistiken , Freiburg in Breisgau : Albert-Ludwig-Universität .
   Google Scholar
• Friedrich , K. O. 1989 . A Berry-Esseen bound for independent random variables . Ann. Statist. , 17 : 170 – 18 .
   Web of Science ®Google Scholar
• Helmers , R. 1981 . A Berry-Esseen theorem for linear combinations of order statistics . The Ann. Probab. , 9 : 342 – 34 .
   Web of Science ®Google Scholar
• Helmers , R. 1982 . Edgeworth expansions for linear combinations of order statistics , Amsterdam : Math. Centre Tracts 105 .
   Google Scholar
• Helmers , R. and Hušková , M. . Berry-Esseen bounds for L-statistics with unbounded weight functions . Proc. Third Prague Symp. on Asymptotic Statistics . pp. 93 – 10 .
   Google Scholar
• Helmers , R. and Hušková , M. 1986 . “ Berry-Esseen bounds for L-statistics with unbounded weight functions ” . Amsterdam : Centre for Mathematics and Computer Science . Report MS-R8611
   Google Scholar
• De Jager , N. G. , Pap , G. and van Zuijlen , M. C. A. 1997 . Facts, phantasies and a new proposal concerning the Stringer bound . Computers Math. Applic. , 33 : 37 – 5 .
   Google Scholar
• Leslie , D. A. , Teitlebaum , A. D. and Anderson , R. J. 1980 . “ Dollar-Unit Sampling-A Practical Guide for Auditors ” . London : Piitman .
   Google Scholar
• Mason , M. M. 1981 . Asymptotic normality of linear combinations of order statistics with a smooth score function . Ann. Statist. , 9 : 899 – 90 .
   Web of Science ®Google Scholar
• Pap , G. and van Zuijlen , M. C. A. 1994 . On the Stringer bound in case of uniform taintings . Computers Math. Applic. , 29 : 51 – 59 .
   Google Scholar
• Pap , G. and van Zuijlen , M. C. A. 1996 . On the asymptotic behaviour of the Stringer bound . Statistica Neerlandica , 50 : 367 – 38 .
   Google Scholar
• Parzen , E. 1979 . Nonparametric statistical data modelling . JASA , 74 : 105 – 12 .
   Web of Science ®Google Scholar
• Reiss , R.-D. 1989 . “ Approximate distributions of order statistics ” . New York Berlin Heidelberg : Springer-Verlag .
   Google Scholar
• Shorack , G. R. and Wellner , J. A. 1986 . “ Empirical processes with applications to statistics ” . New York : John Wiley and Sons .
   Google Scholar
• Schuster , E. F. 1984 . Classification of probability laws by tail behavior . JASA , 79 : 936 – 939 .
   Web of Science ®Google Scholar
• Serfling , R. J. 1980 . “ Approximation Theorems of Mathematical Statistics ” . New York : John Wiley and Sons .
   Google Scholar
• 1989 . Statistical Models and Analysis in Auditing . Statistical Science , 4 : 2 – 3 .
   Google Scholar
• Van Zwet , W. R . 1980 . A strong law for linear functions of order statistics . The Ann. Probab. , 8 : 986 – 99 .
   Web of Science ®Google Scholar
• van Zwet , W. R. 1984 . A Berry-Esseen bound for symmetric statistics . Z. Wahrsch. verw. Gebiete , 66 : 425 – 44 .
   Google Scholar