A scalable bootstrap for massive data

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 76, Issue 4, 2014, Pages 795-816

  Kleiner, Ariel ^a   Talwalkar, Ameet ^a   Sarkar, Purnamrita ^a   Jordan, Michael I ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Bootstrap; Computational efficiency; Estimator quality assessment; Massive data; Resampling

Indexed keywords

EID: 84905910853     PISSN: 13697412     EISSN: 14679868     Source Type: Journal    
DOI: 10.1111/rssb.12050     Document Type: Article

References (27)

1. Bickel, P. J. and Freedman, D. A. (1981) Some asymptotic theory for the bootstrap. Ann. Statist., 9, 1196-1217.
2. Bickel, P. J., Gotze, F. and van Zwet, W. (1997) Resampling fewer than n observations: gains, losses, and remedies for losses. Statist. Sin., 7, 1-31.
3. Bickel, P. J. and Sakov, A. (2002) Extrapolation and the bootstrap. Sankhya A, 64, 640-652.
4. Bickel, P. J. and Sakov, A. (2008) On the choice of m in the m out of n bootstrap and confidence bounds for extrema. Statist. Sin., 18, 967-985.
5. Bickel, P. J. and Yahav, J. A. (1988) Richardson extrapolation and the bootstrap. J. Am. Statist. Ass., 83, 387-393.
6. Diaconis, P. and Efron, B. (1983) Computer-intensive methods in statistics. Scient. Am., 248, 96-108.
7. Efron, B. (1979) Bootstrap methods: another look at the jackknife. Ann. Statist., 7, 1-26.
8. Efron, B. (1988) More efficient bootstrap computations. J. Am. Statist. Ass., 85, 79-89.
9. Efron, B. and Tibshirani, R. (1993) An Introduction to the Bootstrap. New York: Chapman and Hall.
10. Frank, A. and Asuncion, A. (2010) UCI machine learning repository. University of California, Irvine. (Available from http://archive.ics.uci.edu/ml.)
11. Giné, E. and Zinn, J. (1990) Bootstrapping general empirical measures. Ann. Probab., 18, 851-869.
12. Hahn, J. (1995) Bootstrapping quantile regression estimators. Econmetr. Theor., 11, 105-121.
13. Hall, P. (1992) The Bootstrap and Edgeworth Expansion. New York: Springer.
14. Hall, P. and Mammen, E. (1994) On general resampling algorithms and their performance in distribution estimation. Ann. Statist., 22, 2011-2030.
15. Kunsch, H. R. (1989) The jacknife and the bootstrap for general stationary observations. Ann. Statist., 17, 1217-1241.
16. Lahiri, S. N., Spiegelman, C., Appiah, J. and Rilett, L. (2012) Gap bootstrap methods for massive data sets with an application to transportation engineering. Ann. Appl. Statist., 6, 1552-1587.
17. Liu, R. Y. and Singh, K. (1992) Moving blocks jackknife and bootstrap capture weak dependence. In Exploring the Limits of the Bootstrap (edsR. LePage and L. Billard ), pp. 225-248. New York: Wiley.
18. Nocedal, J. and Wright, S. J. (2006) Numerical Optimization. New York: Springer.
19. Politis, D. N. and Romano, J. P. (1994) The stationary bootstrap. J. Am. Statist. Ass., 89, 1303-1313.
20. Politis, D., Romano, J. and Wolf, M. (1999) Subsampling. New York: Springer.
21. Putter, H. and van Zwet, W. R. (1996) Resampling: consistency of substitution estimators. Ann. Statist., 24, 2297-2318.
22. Samworth, R. (2003) A note on methods of restoring consistency to the bootstrap. Biometrika, 90, 985-990.
23. Shao, J. (2003) Mathematical Statistics, 2nd edn. New York: Springer.
24. Tibshirani, R. (1985) How many bootstraps? Technical Report. Department of Statistics, Stanford University, Stanford.
25. van der Vaart, A. W. (1998) Asymptotic Statistics. Cambridge: Cambridge University Press.
26. van der Vaart, A. W. and Wellner, J. A. (1996) Weak Convergence and Empirical Processes. New York: Springer.
27. Zaharia, M., Chowdhury, M., Das, T., Dave, A., Ma, J., McCauley, M., Franklin, M. J., Shenker, S. and Stoica, I. (2012) Resilient distributed datasets: a fault-tolerant abstraction for in-memory cluster computing. USENIX Symp. Networked Systems Design and Implementation.