Computer-intensive methods in statistical analysis: An introduction to the bootstrap, the jackknife, and other household items in a statistician's toolbox

IEEE Signal Processing Magazine

Volumn 15, Issue 1, 1998, Pages 39-55

  Politis, Dimitris N ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTER AIDED ANALYSIS; MONTE CARLO METHODS; PROBABILITY; RANDOM PROCESSES; SAMPLING;

BOOTSTRAP; HIGH SPEED COMPUTERS;

STATISTICAL METHODS;

EID: 0031672709     PISSN: 10535888     EISSN: None     Source Type: Journal    
DOI: 10.1109/79.647042     Document Type: Article

References (58)

1. K. Athreya, Bootstrap of the Mean in the Infinite Variance Case, Ann. Statist., vol. 15, pp. 724-731, 1987.
2. Ph. Barbe and P. Bertail, The Weighted Bootstrap, Lecture Notes in Statistics # 98, Springer Verlag, New York, 1995.
3. R. Beran, Bootstrap Methods in Statistics. Jber. d. Dt. Math.-Verein 86, 14-30, 1984.
4. R. Beran, Discussion to Wu, C.F.J.: Jackknife, Bootstrap and Other Resampling Methods in Regression Analysis, Ann. Statist., vol. 14, 1295-1298, 1986.
5. R. Beran and G.R. Ducharme, Asymptotic Theory for Bootstrap Methods in Statistics, Les Publications CRM, Montreal, 1991.
6. P. Bertail, Second Order Properties of an Extrapolated Bootstrap without Replacement: the i.i.d. and the strong mixing cases, Bernoulli, vol. 3, 149-179, 1997.
7. P. Bertail, D.N. Politis, and J.P. Romano, On Subsampling Estimators with Unknown Rate of Convergence, Technical Report No. 95-20, Dept. of Statistics, Purdue University, 1995.
8. P. Bicke land D. Freedman, Some Asymptotic Theory for the Bootstrap. Ann. Statist., 9, 1196-1217, 1981.
9. P. Bickel, F. Götze, and W.R. van Zwet, Resampling Fewer than n Observations: Gains, Losses and Remedies for Losses, Statist. Sinica. vol. 7, 1-31, 1997.
10. A. Bose, (1988), Edgeworth Correction by Bootstrap in Autoregressions, Ann.Statist., 16, pp. 1709-1722, 1988.
11. A. Bose D.N. Politis, A Review of the Bootstrap for Dependent Samples, in Stochastic Processes and Statistical Inference, B.R. Bhat and B.L.S. Prakasa Rao (Eds.), New Age International Publishers, New Delhi, 1995, pp. 39-51, 1996.
12. E. Carlstein, Resampling Techniques for Stationary Time Series: Some Recent Developments, in New Direction in Time Series Analysis, Brillinger, D.R. et al. (Eds.), Springer Verlag, New York, 1992.
13. T. DiCiccio and J. Romano, A Review of Bootstrap Confidence Intervals (with discussion), J. Roy. Statist. Soc., Ser. B, vol. 50, 338-370, 1988.
14. B. Efron, Bootstrap Methods: Another Look at the Jackknife, Ann. Statist., 7, 1-26, 1979.
15. B. Efron, Computers and the Theory of Statistics: Thinking the Unthinkable, SIAM Review, vol. 21, no. 4, pp. 460-480, 1979.
16. B. Efron, The Jackknife, the Bootstrap, and other Resampling Plans, SIAM NSF-CBMS, Monograph 38, 1982.
17. B. Efron, Computer-intensive Methods in Statistical Regression, SIAM Review, vol. 30, no. 3, pp. 421-449, 1988.
18. B. Efron and G. Gong , A Leisurely Look at the Bootstrap, the Jackknife, and Cross-Validation, Amer. Statistician, vol. 37, no. 1, pp. 36-48, 1983.
19. B. Efron and R.J. Tibshirani, Bootstrap Methods for Standard Errors, Confidence Intervals and Other Measures of Statistical Accuracy, Statist. Sci. 1, 54-77, 1986.
20. B. Efron and R.J. Tibshirani, An Introduction to the Bootstrap, Chapman and Hall, New York, 1993.
21. J. Franke and W. Härdle, On Bootstrapping Kernel Spectral Estimates, Ann.Statist., 20, 121-145, 1992.
22. E. Giné and J. Zinn, Necessary Conditions for the Bootstrap of the Mean, Ann.Statist., vol. 17, pp. 684-691, 1989.
23. F. Götze and H.R. Künsch, Second Order Correctness of the Blockwise Bootstrap for Stationary Observations, Ann. Statist., vol. 24, 1914-1933, 1996.
24. P. Hall, Theoretical Comparison of Bootstrap Confidence Intervals, Ann. Statist., 16, 927-953, 1988.
25. P. Hall, The Bootstrap and Edgeworth Expansion, Springer Verlag, New York, 1992.
26. D.V. Hinkley, Bootstrap methods (with discussion), J. Roy. Statist. Soc., Ser. B, vol. 50, 321-337, 1988.
27. J.S.U. Hjorth, Computer Intensive Statistical Methods: Validation Model Selection and Bootstrap, Chapman and Hall, New York, 1994.
28. J.P. Kreiss and J. Franke, Bootstrapping Stationary Autoregressive Moving Average Models, J. Time Ser. Anal., 13, pp. 297-319, 1992.
29. H.R. Künsch, The Jackknife and the Bootstrap for General Stationary Observations, Ann. Statist 17, 1217-1241, 1989.
30. S.N. Lahiri, Edgeworth Correction by "moving block" Bootstrap for Stationary and Nonstationary Data, in Exploring the Limits of Bootstrap, LePage and Billard (Eds.), John Wiley, pp. 183-214, 1992.
31. C. Léger, D.N. Politis, and J.P. Romano, Bootstrap Technology and Applicatioas, Technometrics, vol. 34, pp. 378-399, 1992.
32. E.L. Lehmann, Theory of Point Estimation, John Wiley, 1983.
33. R. LePage and L. Billard (Eds.), Exploring the Limits of Bootstrap, John Wiley, 1992.
34. H. Li and G.S. Maddala, Bootstrapping Time Series Models, Econometric Rev., vol. 15, no. 2, 1996, pp. 115-158, 1996.
35. R.Y. Liu and K. Singh, Moving Blocks Jackknife and Bootstrap Capture Weak Dependence, in Exploring the limits of bootstrap, LePage and Billard (Eds.), John Wiley, pp. 225-248, 1992.
36. E. Mammen, When Does Bootstrap Work? Asymptotic Results and Simulations, Lecture notes in Statistics # 77, Springer, New York, 1992.
37. R. Miller, Beyond ANOVA: Basics of Applied Statistics, John Wiley, 1986.
38. E. Paparoditis, Bootstrapping Autoregressive and Moving Average Parameter Estimates of Infinite Order Vector Autoregressive Processes. J. Multivar. Anal., vol. 57, pp. 277-296, 1996.
39. D.N. Politi sand J.P. Romano, A Circular Block-Resampling Scheme for Stationary Data, in Exploring the Limits of Bootstrap, LePage and Billard (Eds.), John Wiley, pp. 263-270, 1992
40. D.N. Politis and J.P. Romano, Nonparametric Resampling for Homogeneous Strong Mixing Random Fields, J. Multivar. Anal., vol. 47, no. 2, pp. 301-328, 1993.
41. D.N. Politis and J.P. Romano, Estimating the Distribution of a Studentized Statistic by Subsampling, Bulletin of the International Statistical Institute, 49th Session, Firenze, August 25 - September 2, 1993, Book 2, pp. 315-316, 1993.
42. D.N. Politis and J.P. Romano, The Stationary Bootstrap, J. Amer, Statist. Assoc., vol. 89, no. 4 28, pp. 1303-1313, 1994.
43. D.N. Politis and J.P. Romano, Large Sample Confidence Regions Based on Subsamples under Minimal Assumptions, Ann.Statist., vol. 22, no. 4, 2031-2050, 1994.
44. D.N. Politis and J.P. Romano, Subsampling for Econometric Models-Comments on Bootstrapping Time Series Models, Econometric Rev., vol. 15, no. 2, pp. 169-176, 1996.
45. D.N. Politis and J.P. Romano, and T.-L. Lai, Bootstrap Confidence Bands for Spectra and Cross-Spectra, IEEE Trans. Signal Proc., vol. 40, no. 5, May 1992, pp. 1206-1215, 1992.
46. D.N. Politis, J.P. Romano, and L. You, Uniform Confidence Bands for the Spectrum Based on Subsamples, in Computing Science and Statistics, Proceedings of the 25th Symposium on the Interface, San Diego, California, April 14-17, 1993 [M. Tarter and M. Lock, (Eds.)], The Interface Foundation of North America, pp. 346-351, 1993.
47. M.B. Priestley, Spectral Analysis and Time Series, Academic Press, 1981
48. M. Quenouille, Approximate Tests of Correlation in Time Series, J. Roy. Statist. Soc. (Ser. B), 11, pp. 68-84, 1949.
49. D. Radulovic, The bootstrap of the Mean for Strong Mixing Sequences under Minimal Conditions, Statist. Prob. Letters, 28, pp. 65-72, 1996.
50. K. Singh, On the Asymptotic Accuracy of Efron's Bootstrap, Ann.Statist., 9, 1187-1195, 1981.
51. J. Shao and D. Tu, The Jackknife and Bootstrap., Springer, New York, 1995.
52. M. Sherman and E. Carlstein, Replicate histograms, J. Amer. Statist. Assoc., 91, no. 4 34, 566-576, 1996.
53. J.W.H. Swanepoel, A Review of Bootstrap Methods, South African Statist. J., vol. 24, pp. 1-34, 1990.
54. J. Thomson and A.D. Chave, Jackknifed error estimates for spectra, coherences, and transfer functions, in Advances in Spectrum Analysis and Array Processing, vol. I, S. Haykin (Ed.), Prentice-Hall, New Jersey, 1991.
55. J.W. Tukey, Bias and Confidence in not Quite Large Samples, (abstract), Ann. Math. Statist., 29, p. 614, 1958.
56. C.F.J. Wu, Jackknife, Bootstrap and Other Resampling Methods in Regression Analysis, Ann. Statist., vol. 14, 1261-1295, 1986.
57. G.A. Young, Bootstrap: More than a Stab in the Dark? (with discussion), Statist. Sci. 9, no. 3 3, 382-415, 1994.
58. A.M. Zoubir and B. Boashash, The Bootstrap and its Application in Signal Processing, IEEE Signal Proc. Magazine, 15, No. 1, 56-76, 1998.