Another look at the jackknife: Further examples of generalized bootstrap

Statistics and Probability Letters

Volumn 40, Issue 4, 1998, Pages 307-319

  Chatterjee, Snigdhansu ^a  

^a INDIAN STATISTICAL INSTITUTE   (India)

Author keywords

Bootstrap; Jackknife; Least squares; Many parameter regression; Second order efficiency

Indexed keywords

EID: 0032533058     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0167-7152(98)00116-3     Document Type: Article

References (34)

1. Barbe, P., Bertail, P., 1995. The Weighted Bootstrap, Lecture Notes in Statistics, vol. 98. Springer, New York.
2. Bera, A.K., Higgins, M.L., 1993. A survey of ARCH models: properties, estimation and testing. J. Economic Surveys 7, 305-366.
3. Bickel, P.J., Freedman, D.A., 1983. Bootstrapping regression models with many parameters. In: Bickel, P., Doksum, K., Hodges, Jr. J., (Eds.), Festschrift for Erich L. Lehmann, Wadsworth, Belmont, Calif., pp. 28-48.
4. Bose, A., Chatterjee, S., 1997. Second order comparison of different resampling schemes in linear regression. Tech. Report No. 15/97, Stat-Math Unit, Indian Statistical Institute, Calcutta.
5. Boos, D., Monahan, J.F., 1986. Bootstrap methods using prior information. Biometrika 73, 77-83.
6. Chatterjee, S., 1997. Generalized bootstrap in regression models with many parameters. Tech. Report No. 2/97, Stat-Math Unit, Indian Statistical Institute, Calcutta.
7. Efron, B., 1979. Bootstrap methods: another look at the jackknife. Ann. Statist. 7, 101-118.
8. Efron, B., 1982. The Jackknife, the Bootstrap and Other Resampling Plans. SIAM, Philadelphia.
9. Freedman, D.A., 1981. Bootstrapping regression models. Ann. Statist. 9, 1218-1228.
10. Härdle, W., Marron, S., 1991. Bootstrap simultaneous error bars for non-parametric regression. Ann. Statist. 19, 778-796.
11. Hinkley, D.V., 1977. Jackknifing in unbalanced situations. Technometrics 19, 285-292.
12. Liu, R.Y., 1988. Bootstrap procedures under some non-i.i.d. models. Ann. Statist. 16, 1696-1708.
13. Liu, R.Y., Singh, K., 1992. Efficiency and robustness in resampling. Ann. Statist. 20, 370-384.
14. Lo, A.Y., 1987. A large sample study of the Bayesian bootstrap. Ann. Statist. 15, 360-375.
15. Lo, A.Y., 1991. Bayesian bootstrap clones and a biometry function. Sankhya, Ser. A 53, 320-333.
16. Mammen, E., 1989. Asymptotics with increasing dimension for robust regression with applications to the bootstrap, Ann. Statist. 17, 382-400.
17. Mammen, E., 1992. When does Bootstrap Work? Asymptotic Results and Simulations, Lecture Notes in Statistics, vol. 77. Springer, New York.
18. Mammen, E., 1993. Bootstrap and wild bootstrap for high dimensional linear models. Ann. Statist. 21, 255-285.
19. 2/n is large, I: consistency. Ann. Statist. 12, 1298-1309.
20. 2/n is large, I: asymptotic normality. Ann. Statist. 13, 1403-1417.
21. Portnoy, S., 1988. Asymptotic behaviour of the empirical distribution of M-estimator residuals from a regression model with many parameters. Ann. Statist. 14, 1152-1170.
22. Praestgaard, J., Wellner, J.A., 1993. Exchangeably weighted bootstrap of the general empirical process. Ann. Probab. 21, 2053-2086.
23. Quenouille, M., 1956. Notes on bias in estimation. Biometrica 43, 353-360.
24. Rubin, D., 1981. The Bayesian bootstrap. Ann. Statist. 9, 130-134.
25. Shao, J., 1987. Sampling and resampling: an efficient approximation to jackknife variance estimators in linear models. Chinese J. Appl. Prob. Statist. 3, 368-379.
26. Shao, J., 1988. Consistency of the jackknife estimators of the variance of sample quantiles. Comm. Statist. A 17, 3017-3028.
27. Shao, J., 1989. The efficiency and consistency of approximations to the jackknife variance estimators. J. Amer. Statist. Assoc. 84, 114-119.
28. Shao, J., Tu, D., 1995. The Jackknife and the Bootstrap. Springer, New York.
29. Shao, J., Wu, C.F.J., 1987. Heteroskedasticity-robustness of jackknife variance estimators in linear models. Ann. Statist. 15, 1563-1579.
30. Shao, J., Wu, C.F.J., 1989. A general theory for jackknife variance estimation. Ann. Statist. 17, 1176-1197.
31. Weng, C.S., 1989. On a second order asymptotic property of the Bayesian bootstrap mean. Ann. Statist. 17, 705-710.
32. Wu, C.F.J., 1986. Jackknife, bootstrap and other resampling methods in regression analysis (with discussion). Ann. Statist. 14, 1295.
33. Wu, C.F.J., 1990. On the asymptotic properties of the jackknife histogram. Ann. Statist. 18, 1438-1452.
34. Zheng, Tu, 1988. Random weighting method in regression models. Sci. Sinica Ser. A 31, 1442-1459.