Empirical edgeworth expansions for symmetric statistics

Annals of Statistics

Volumn 26, Issue 4, 1998, Pages 1540-1569

  Putter, Hein ^a   Van Zwet, Willem R ^b  

^a UNIVERSITY OF AMSTERDAM   (Netherlands)

^b LEIDEN UNIVERSITY   (Netherlands)

Author keywords

Bootstrap; Edgeworth expansion; Hoeffding's decomposition; Jackknife

Indexed keywords

EID: 0041171600     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1024691253     Document Type: Article

References (13)

1. BENTKUS, V., GÖTZE, F. and VAN ZWET, W. R. (1997). An Edgeworth expansion for symmetric statistics. Ann. Statist. 25 851-896.
2. BICKEL, P. J., GÖTZE, F. and VAN ZWET, W. R. (1986). The Edgeworth expansion for U-statistics of degree 2. Ann. Statist. 14 1463-1484.
3. CALLAERT, H. and VERAVERBEKE, N. (1981). The order of the normal approximation for a Studentized U-statistic. Ann. Statist. 9 194-200.
4. DHARMADHIKARI, S. W., FABIAN, V. and JOGDEO, K. (1968). Bounds on the moments of martingales. Ann. Math. Statist. 39 1719-1723.
5. HELMERS, R. (1991). On the Edgeworth expansion and the bootstrap approximation for a Studentized U-statistic. Ann. Statist. 19 470-484.
6. HOEFFDING, W. (1948). A class of statistics with asymptotically normal distribution. Ann. Math. Statist. 19 293-325.
7. JANSSEN, P. (1978). The Berry-Esseen theorem and an asymptotic expansion for U-statistics, Ph.D. thesis, Limburg Univ. Centre (in Dutch).
8. PUTTER, H. (1994). Consistency cf resampling methods. Ph.D. thesis, Univ. Leiden.
9. QUENOUILLE, M. H. (1949). Approximate tests of correlation in time series. J. Roy. Statist. Soc. Ser. B 11 68-84.
10. QUENOUILLE, M. H. (1956). Notes on bias in estimation. Biometrika 43 353-360.
11. TUKEY, J. W. (1958). Bias and confidence in not-quite large samples. Ann. Math. Statist. 29 614 (abstract).
12. VAN ZWET, W. R. (1984). A Berry-Esseen bound for symmetric statistics. Z. Wahrsch. Verw. Gebiete 66 425-440.
13. VON BAHR, B. and ESSEEN C. G. (1965). Inequalities for the rth absolute moment of a sum of random variables, 1 ≤ r ≤ 2. Ann. Math. Statist. 36 299-303.