Bootstrap methods: A review

Frontiers in Statistics: Dedicated to Peter John Bickel in Honor of his 65th Birthday

Volumn , Issue , 2006, Pages 231-255

  Lahiri, S N ^a  

^a Iowa State University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84967592241     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/9781860948886_0011     Document Type: Chapter

References (93)

1. Anderson, T. W. (1971). The statistical analysis of time series. Wiley, New York.
2. Arcones, M. A. and Giné, E. (1989). The bootstrap of the mean with arbitrary bootstrap sample size. Annales de l'lnstitut Henri Poincare, Section B, Calcul des Probabilities et Statistique 25 457-481. (Corrections: 1991, Vol. 27, p583-595).
3. Athreya, K. B., and Fuh, C. D. (1992). Bootstrapping Markov chains: Countable case. Journal of Statistical Planning and Inference 33 311-331.
4. Athreya, K. B. and Ney, P. (1978). A new approach to the limit theory of recurrent Markov chains. Transactions of the American Mathematical Society 245, 493-501.
5. Babu, G. J. and Singh, K. (1984). On one term Edgeworth correction by Efron's bootstrap. Sankhya, Series A 46, 219-232.
6. Bickel, P. J. and Freedman, D. A. (1981). Some asymptotic theory for the bootstrap. Annals of Statistics 9, 1196-1217.
7. Bickel, P. J., Götze, F., and van Zwet, W. R. (1997). Resampling fewer than n observations: Gains, losses, and remedies for losses. Statistica Sinica 7, 1-32.
8. Bose, A. (1988). Edgeworth correction by bootstrap in autoregressions. Annals of Statistics 16, 1709-1722.
9. Brockwell, P. J., and Davis, R. A. (1996). Introduction to time series and forecasting. Springer-Verlag Inc. New York.
10. Bühlmann, P. (1997). Sieve bootstrap for time series. Bernoulli 3, 123-148.
11. Bühlmann, P. (2002). Sieve bootstrap with variable-length Markov chains for stationary categorical time series. With comments and a rejoinder by the author. Journal of the American Statistical Association 97, 458, 443-471.
12. Bühlmann, P. and Künsch, H. R. (1999). Block length selection in the bootstrap for time series. Computational Statistics and Data Analysis 31, 295-310.
13. Carlstein, E. (1986). The use of subseries values for estimating the variance of a general statistic from a stationary sequence. Annals of Statistics 14, 1171-1179.
14. Carlstein, E., Do, K-A., Hall, P., Hesterberg, T., and Künsch, H. R. (1998). Matched-block bootstrap for dependent data. Bernoulli 4, 305-328
15. Chatterjee, S. and Bose, A. (2002). Dimension asymptotics for generalised bootstrap in linear regression. Annals of the Institute of Statistical Mathematics 54 367-381.
16. Choi, E. and Hall, P. (2000). Bootstrap confidence regions computed from autoregressions of arbitrary order. Journal of the Royal Statstical Society, Series B 62, 461-477.
17. Dahlhaus, R. and Janas, D. (1996). A frequency domain bootstrap for ratio statistics in time series analysis. Annals of Statistics 24, 1934-1963.
18. Datta, S. (1995). Limit theory and bootstrap for explosive and partially explosive autoregression. Stochastic Processes and their Applications 57, 285-304.
19. Datta, S. (1996). On asymptotic properties of bootstrap for AR(1) processes. Journal of Statistical Planning and Inference 53, 361-374.
20. Datta, S. and McCormick, W. P. (1995a). Bootstrap inference for a first-order autoregression with positive innovations. Journal of the American Statistical Association 90, 1289-1300.
21. Datta, S. and McCormick, W. P. (1995b). Some continuous Edgeworth expansions for Markov chains with applications to bootstrap. Journal of Multivariate Analysis 52, 83-106.
22. Davison, A. C. and Hinkley, D. V. (1997). Bootstrap methods and their application. Cambridge University Press, Cambridge, UK.
23. Dobrushin, R. L., and Major, P. (1979). Non-central limit theorems for non-linear functionals of Gaussian fields. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 50, 27-52.
24. Efron, B. (1979). Bootstrap methods: Another look at the jackknife. Annals of Statistics 7, 1-26.
25. Efron, B. (1987). Better bootstrap confidence intervals. (With comments and a rejoinder by the author). Journal of the American Statistical Association 82, 171-200.
26. Efron, B. (1992). Jackknife-after-bootstrap standard errors and influence functions (Disc: p 111-127). Journal of the Royal Statistical Society, Series B 54, 83-111.
27. Efron, B. and Tibshirani, R. J. (1986). Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy (C/R: p75-96). Statistical Science 1, 54-75.
28. Efron, B. and Tibshirani, R. J. (1993). An introduction to the bootstrap. Chapman & Hall Ltd, New York.
29. Fukuchi, J. I. (1994). Bootstrapping extremes of random variables. Ph.D. Dissertation. Iowa State University, Ames, IA.
30. Falk, M. and Reiss, R.-D. (1989). Weak convergence of smoothed and nonsmoothed bootstrap quantile estimates. Annals of Probability 17 362- 371.
31. Ferretti, N. and Romo, J. (1996). Unit root bootstrap tests for AR(1) models. Biometrika 83 849-860.
32. Franke, J.and Härdle, W. (1992) On bootstrapping kernel spectral estimates. Annals of Statistics 20, 121-145.
33. Freedman, D. A. (1981). Bootstrapping regression models. Annals of Statistics 9, 1218-1228.
34. Freedman, D. A. and Peters, S. C. (1984). Bootstrapping a regression equation: Some empirical results. Journal of the American Statistical Association 79, 97-106.
35. Ghosh, M., Parr, W.C., Singh, K. and Babu, G. J. (1984). A Note on Bootstrapping the Sample Median. Annals of Statistics 12, 1130-1135.
36. Giné, E. and Zinn, J. (1989). Necessary conditions for the bootstrap of the mean. Annals of Statistics 17, 684-691.
37. Götze, F. and Kiinsch, H. R. (1996). Second-order correctness of the blockwise bootstrap for stationary observations. Annals of Statistics 24, 1914- 1933.
38. Heimann, G. and Kreiss, J-P. (1996). Bootstrapping general first order autoregression. Statistics & Probability Letters 30 87-98.
39. Hall, P. (1988). Theoretical comparison of bootstrap confidence intervals (C/R: p953-985). Annals of Statistics 16, 927-953.
40. Hall, P. (1992). The bootstrap and Edgeworth expansion. Springer-Verlag Inc. New York.
41. Hall, P., DiCiccio, T. J. and Romano, J. P. (1989). On smoothing and the bootstrap. Annals of Statistics 17, 692-704.
42. Hall, P., Horowitz, J. L., and Jing, B-Y. (1995). On blocking rules for the bootstrap with dependent data. Biometrika 82, 561-574.
43. Hall, P., Jing, B.-Y., and Lahiri, S. N.(1998). On the sampling window method for long-range dependent data. Statistica Sinica 8, 1189-1204.
44. Helmers, R. (1991). On the Edgeworth expansion and the bootstrap approximation for a studentized [/-statistic. Annals of Statistics 19, 470-484.
45. Ho, Y. H. S. and Lee, S. M. S. (2005). Iterated smoothed bootstrap confidence intervals for population quantiles. Annals of Statistics 33 (In press).
46. Hurvich C. M. and Zeger, S. L. (1987). Frequency domain bootstap methods for time series. Statistics and Operations Reserach working paper. New York university, New York.
47. Koul, H. L. and Lahiri, S. N. (1994). On bootstrapping M-estimated residual processes in multiple linear regression models. Journal of Multivariate Analysis 49, 255-265.
48. Kreiss, J-P. and Franke, J. (1992). Bootstrapping stationary autoregressive moving-average models. Journal of Time Series Analysis 13, 297-317.
49. Kreiss, J-P. and Paparoditis, E. (2003). Autoregressive-aided periodogram bootstrap for time series. Annals of Statistics 31, 1923-1955.
50. Kulperger, R. J. and Prakasa Rao, B. L. S. (1989). Bootstrapping a finite state Markov chain. Sankhya, Series A 51 178-191.
51. Lahiri, S. N. (1991). Second order optimality of stationary bootstrap. Statistics and Probability Letters 11, 335-341.
52. Lahiri, S. N. (1992a). Bootstrapping M-estimators of a multiple regression parameter. Annals of Statistics 20, 1548-1570.
53. Lahiri, S. N. (1992b). Edgeworth correction by 'moving block bootstrap' for stationary and nonstationary data. In Exploring the limits of bootstrap. Eds. R. Lepage and L. Billard, Wiley, NY, 183-214.
54. Lahiri, S. N. (1994a). Rates of bootstrap approximation for the mean of lattice variables. Sankhya, Ser. A. 56, 77-89.
55. Lahiri, S. N. (1994b). Two term Edgeworth expansion and bootstrap approximation for multivariate studentized M-estimators. Sankhya, Ser. A. 56, 201-226.
56. Lahiri, S. N. (1996). On Edgeworth expansions and the moving block bootstrap for studentized M-estimators in multiple linear regression models. Journal of Multivariate Analysis 56, 42-59.
57. Lahiri, S. N. (1999a). Theoretical comparison of block bootstrap methods. Annals of Statistics 27, 386-404.
58. Lahiri, S.N. (1999b). Asymptotic distribution of the empirical spatial cumulative distribution function predictor and prediction bands based on a subsampling Method. Probability Theory and Related Fields 114, 55-84.
59. Lahiri, S. N. (2002). On the Jackknife after Bootstrap method for dependent data and its consistency properties. Econometric Theory 18, 79-98.
60. Lahiri, S. N. (2003a). Resampling methods for dependent data. Springer-Verlag Inc., New York.
61. Lahiri, S. N. (2003b). A necessary and sufficient condition for asymptotic independence of discrete Fourier transforms under short- and long-range dependence. Annals of Statistics 31, 613-641.
62. Lahiri, S.N. (2003c). Validity of a block bootstrap method for irregularly spaced spatial data under nonuniform stochastic designs. Preprint, Department of Statistics, Iowa State University, Ames, IA.
63. Lahiri, S. N., Furukawa, K., and Lee, Y-D. (2003). A nonparametric plug-in method for selecting the optimal block length. Preprint, Department of Statistics, Iowa State University, Ames, IA.
64. Lahiri, S. N., Kaiser, M. S., Cressie, N., and Hsu, N-J. (1999). Prediction of spatial cumulative distribution functions using subsampling (with discussion.) Journal of the American Statistical Association 94, 86 -110.
65. Lahiri, S. N. (2005). A note on the subsampling method under long range dependence. Preprint, Department of Statistics, Iowa State University, Ames, IA.
66. Lahiri, S.N. and Zhu, J. (2005). Resampling methods for spatial regression models under a class of stochastic designs. Preprint, Department of Statistics, Iowa State University, Ames, IA.
67. Lee, Y-D. and Lahiri, S.N. (2002). Least squares variogram fitting by spatial subsampling. Journal of the Royal Statistical Society, Series B 64, 837- 854.
68. Lee, S. M. S. and Young, G. A. (1995). Asymptotic iterated bootstrap confidence intervals. Annals of Statistics 23, 1301-1330.
69. Liu, R. Y., and Singh, K. (1992a). Moving blocks jackknife and bootstrap capture weak dependence. In Exploring the Limits of Bootstrap Ed. R.Lepage and L. Billard. 225-248.
70. Liu, R. Y., and Singh, K. (1992b). Efficiency and robustness in resampling. Annals of Statistics 20, 370-384.
71. Loh, W-Y. (1987). Calibrating confidence coefficients. Journal of the American Statistical Association 82, 155-162.
72. Nordman, D. and Lahiri, S. N. (2004). On optimal spatial subsample size for variance estimation. Annals of Statistics. 32 1981-2027.
73. Nordman, D., Lahiri, S.N., and Sibbertsen, P. (2004). Empirical likelihood confidence intervals for the mean of a long range dependent process. Preprint, Department of Statistics, Iowa State University, Ames, IA.
74. Paparoditis, E. and Politis, D. N. (2001a). Tapered block bootstrap. Biometrika 88 1105-1119.
75. Paparoditis, E., and Politis, D. N. (2001b). A Markovian local resampling scheme for nonparametric estimators in time series analysis. Econometric Theory 17, 540-566.
76. Percival, D. B., Sardy, S., and Davison, A. C. (2000). Wavestrapping time series: adaptive wavelet-based bootstrapping. In Nonlinear and nonsta- tionary signal processing (Cambridge, 1998). p. 442-471, Cambridge Univ. Press, Cambridge.
77. Politis, D. N., Paparoditis, E., and Romano, J. P. (1998). Large sample inference for irregularly spaced dependent observations based on subsampling. Sankhya, Series A 60, 274-292.
78. Politis, D. N., Paparoditis, E., and Romano, J. P. (1999). Resampling marked point processes. In Multivariate Analysis, Design of Experiments, and Survey Sampling: A tribute to J.N. Srivastava S. Ghosh (Ed.). Mercel Dekker, New York. P. 163-185.
79. Politis, D. N. and Romano, J. P. (1992). A circular block-resampling procedure for stationary data. In Exploring the Limits of Bootstrap. 263-270.
80. Politis, D. N. and Romano, J. P. (1993). Nonparametric resampling for homogeneous strong mixing random fields. Journal of Multivariate Analysis. 47, 301-328.
81. Politis, D. N., and Romano, J. P. (1994). The stationary bootstrap. Journal of the American Statistical Association 89, 1303-1313.
82. Politis, D.N. and White, H. (2003). Automatic block-length selection for the dependent bootstrap. Preprint Department of Mathematics, University of California at San Diego, LaJolla, CA.
83. Politis, D. N., Romano, J. P., and Wolf, M. (1999). Subsampling. Springer-Verlag Inc., New York.
84. Sakov, A. and Bickel, P. J. (1999). Choosing m in the m out of n bootstrap. ASA Proceedings of the Section on Bayesian Statistical Science 125-128.
85. Shao, J. and Tu, D. (1995). The jackknife and bootstrap. Springer-Verlag Inc. New York.
86. Shorack, G. R. (1982). Bootstrapping robust regression. Communications in Statistics, Part A - Theory and Methods 11, 961-972
87. Sherman, M. and Carlstein, E. (1994). Nonparametric estimation of the moments of a general statistic computed from spatial data. Journal of the American Statistical Association 89, 496-500.
88. Singh, K. (1981). On the asymptotic accuracy of Efron's bootstrap. Annals of Statistics 9, 1187-1195.
89. Sjöstedt-DeLuna, S. and Young, G. A. (2003). The bootstrap and Kriging prediction intervals. Scandinavian Journal of Statistics 30, 175-192.
90. Swanepoel, J. W. H., and van Wyk, J. W. J. (1986). The bootstrap applied to power spectral density function estimation. Biometrika 73, 135-141.
91. Taqqu, M. S. (1975). Weak convergence to fractional Brownian motion and to the Rosenblatt process. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 31, 287-302.
92. Taqqu, M. S. (1979). Convergence of integrated processes of arbitrary hermite rank. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 50, 53-83.
93. Zhu, J. and Lahiri, S. N. (2005). Weak convergence of the spatial empirical process and its bootstrap version. Statistical Inference from Stochastic Processes. (In press).