Prepivoting test statistics: A bootstrap view of asymptotic refinements

Journal of the American Statistical Association

Volumn 83, Issue 403, 1988, Pages 687-697

  Beran, Rudolf ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Asymptotic test; Bartlett adjustment; Behrens Fisher problem; Bootstrap test; Edgeworth expansion; Error in rejection probability

Indexed keywords

EID: 84929837036     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1988.10478649     Document Type: Article

References (19)

1. Abramovitch, L., and Singh, K. (1985), “Edgeworth Corrected Pivotal Statistics and the Bootstrap,” The Annals of Statistics, 13, 116–132.
2. Bahadur, R. R., and Savage, L. J. (1956), “The Nonexistence of Certain Statistical Procedures in Nonparametric Problems,” Annals of Mathematical Statistics, 27, 1115–1122.
3. Barndorff-Nielsen, O. E., and Cox, D. R. (1984), “Bartlett Adjustments to the Likelihood Ratio Statistic and the Distribution of the Maximum Likelihood Estimator,” Journal of the Royal Statistical Society, Ser. B, 46, 483–495.
4. Bartlett, M. S. (1937), “Properties of Sufficiency and Statistical Tests,” Proceedings of the Royal Statistical Society, Ser. A, 160, 268–282.
5. Beran, R. (1984), “Jackknife Approximations to Bootstrap Estimates,” The Annals of Statistics, 12, 101–118.
6. —— (1986), “Simulated Power Functions,” The Annals of Statistics, 14, 151–173.
7. —— (1987), “Prepivoting to Reduce Level Error of Confidence Sets,” Biometrika, 74, 457–468.
8. Bhattacharya, R. N., and Ghosh, J. K. (1978), “On the Validity of the Formal Edgeworth Expansion,” The Annals of Statistics, 6, 435–451.
9. Bickel, P. J., and Ghosh, J. K. (1988), “A Decomposition for the Likelihood Ratio Statistic and the Bartlett Correction—A Bayesian Approach,” Technical Report 111, University of California, Berkeley, Dept. of Statistics.
10. Chernoff, H. (1949), “Asymptotic Studentization in Testing of Hypotheses,” Annals of Mathematical Statistics, 20, 268–278.
11. Efron, B. (1979), “Bootstrap Methods: Another Look at the Jackknife,” The Annals of Statistics, 7, 1–26.
12. Hall, P. (1983), “Inverting an Edgeworth Expansion,” The Annals of Statistics, 11, 569–576.
13. Huber, P. J. (1973), “Robust Regression: Asymptotics, Conjectures, and Monte Carlo,” The Annals of Statistics, 1, 799–821.
14. Johnson, N. J. (1978), “Modified t Tests and Confidence Intervals for Asymmetrical Populations,” Journal of the American Statistical Association, 73, 536–544.
15. Loh, W.-Y. (1985), “A New Method for Testing Separate Families of Hypotheses,” Journal of the American Statistical Association, 80, 362–368.
16. Welch, B. L. (1937), “The Significance of the Difference Between Two Means When the Population Variances Are Unequal,” Biometrika, 29, 350–362.
17. —— (1947), “The Generalization of ‘Student’s’ Problem When Several Different Population Variances Are Involved,” Biometrika, 34, 2835.
18. Wilks, S. S. (1938), “The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypothesis,” Annals of Mathematical Statistics, 9, 60–62.
19. Withers, C. S. (1983), “Expansion for the Distribution and Quantiles of a Regular Functional of the Empirical Distribution With Applications to Nonparametric Confidence Intervals,” The Annals of Statistics, 11, 577–587.