A nonparametric plug-in rule for selecting optimal block lengths for block bootstrap methods

Statistical Methodology

Volumn 4, Issue 3, 2007, Pages 292-321

  Lahiri, S N ^a   Furukawa, K ^a   Lee, Y D ^b  

^a Department of Statistics Center for Statistics and Applications in Forensic Evidence Iowa State University 2438 Osborn Dr Ames   (United States)

^b Seoul National University   (South Korea)

Author keywords

Bias estimation; Consistency; Jackknife after bootstrap method; Mean squared error; Stationarity

Indexed keywords

EID: 34248582000     PISSN: 15723127     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.stamet.2006.08.002     Document Type: Article

References (30)

1. Bühlmann P. Blockwise bootstrapped empirical process for stationary sequences. Ann. Statist. 22 (1994) 995-1012
2. Bühlmann P., and Künsch H.R. Block length selection in the bootstrap for time series. Comput. Statist. Data Anal. 31 (1999) 295-310
3. Carlstein E. The use of subseries methods for estimating the variance of a general statistic from a stationary time series. Ann. Statist. 14 (1986) 1171-1179
4. Carlstein E., Do K.-A., Hall P., Hesterberg T., and Künsch H.R. Matched-block bootstrap for dependent data. Bernoulli 4 (1998) 305-328
5. Davison A.C., and Hall P. On studentizing and blocking methods for implementing the bootstrap with dependent data. Aust. J. Statist. 35 (1993) 215-224
6. Efron B. Bootstrap methods: Another look at the jackknife. Ann. Statist. 7 (1979) 1-26
7. Efron B. Jackknife-after-bootstrap standard errors and influence functions (with discussion). J. Roy. Statist. Soc. Ser. B 54 (1992) 83-111
8. Götze F., and Hipp C. Asymptotic expansions for sums of weakly dependent random vectors. Zieb Wahr. Verw Gebiete 64 (1983) 211-239
9. Götze F., and Künsch H.R. Second-order correctness of the blockwise bootstrap for stationary observations. Ann. Statist. 24 (1996) 1914-1933
10. Hall P. Resampling a coverage pattern. Stochastic. Process. Appl. 20 (1985) 231-246
11. Hall P. The Bootstrap and Edgeworth Expansion (1992), Springer-Verlag Inc., New York
12. Hall P., Horowitz J.L., and Jing B.-Y. On blocking rules for the bootstrap with dependent data. Biometrika 82 (1995) 561-574
13. Hall P., Lahiri S.N., and Polzehl J. On bandwidth choice in nonparametric regression with both short- and long-range dependent errors. Ann. Statist. 23 (1995) 1331-1349
14. Hall P., Lahiri S.N., and Truong Y.K. On bandwidth choice for density estimation with dependent data. Ann. Statist. 23 (1995) 2241-2226
15. Hall P., and Jing B.-Y. On sample reuse methods for dependent data. J. Roy. Statist. Soc. Ser. B 58 (1996) 727-737
16. Künsch H.R. The jackknife and the bootstrap for general stationary observations. Ann. Statist. 17 (1989) 1217-1261
17. Lahiri S.N. Second order optimality of stationary bootstrap. Statist. Probab. Lett. 11 (1991) 335-341
18. Lahiri S.N. On Edgeworth expansion and moving block bootstrap for studentized M-estimators in multiple linear regression models. J. Multivariate Anal. 56 (1996) 42-59
19. Lahiri S.N. Theoretical comparisons of block bootstrap methods. Ann. Statist. 27 (1999) 386-404
20. Lahiri S.N. On the jackknife-after-bootstrap method for dependent data and its consistency properties. Econometric Theory 18 (2002) 79-98
21. Lahiri S.N. Consistency of the jackknife-after-bootstrap variance estimator for block bootstrap quantiles of a studentized statistic. Ann. Statist. 33 (2005) 2475-2506
22. Liu R.Y., and Singh K. Moving blocks jackknife and bootstrap capture weak dependence. In: Lepage R., and Billard L. (Eds). Exploring the Limits of Bootstrap (1992), Wiley, New York 225-248
23. Naik-Nimbalkar U.V., and Rajarshi M.B. Validity of blockwise bootstrap for empirical processes with stationary observations. Ann. Statist. 22 (1994) 980-994
24. Paparoditis E., and Politis D.N. Tapered block bootstrap. Biometrika 88 (2001) 1105-1119
25. Politis D., and Romano J.P. A circular block resampling procedure for stationary data. In: Lepage R., and Billard L. (Eds). Exploring the Limits of Bootstrap (1992), Wiley, New York 263-270
26. Politis D., and Romano J.P. Large sample confidence regions based on subsamples under minimal assumptions. Ann. Statist. 22 (1994) 2031-2050
27. Politis D., and Romano J.P. Stationary bootstrap. J. Amer. Statist. Assoc. 89 (1994) 1303-1313
28. Politis D., and Romano J.P. Bias-corrected nonparametric spectral estimation. J. Time Ser. Anal. 16 (1995) 67-103
29. D. Politis, H. White, Automatic block length selection for the dependent bootstrap. Department of Mathematics, University of California at San Diego, LaJolla, CA. 2003. Preprint
30. Lahiri S.N. Resampling Methods for Dependent Data (2003), Springer-Verlag Inc., NY