Bootstrapping, and Other Resampling Methods

04 Aug 2010 17:50

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Bootstrapping is a way of figuring out the properties of statistical estimators (and other procedures, like hypothesis tests) by simulation. What we would really like to know his how different our answers could have been, if we re-ran our experiment. We can't actually do this, but we can fit a model to our data and simulate from it, and see what answer we'd get from the simulations. We can even do this from exceedingly general non-parametric estimates, like re-sampling the original data. This is a brilliant idea, and my default way of handling the uncertainty of estimation in complex models or with complex systems. But having just 3500 words on this for a magazine, I feel absolutely no inclination to explain myself further. (I will link from here to the article when I can.)

I most interested in resampling techniques for dependent data, and would be ecstatic if I could figure out a non-parametric bootstrap for networks. — Presumably universal prediction algorithms could be used for this purpose?

See also: Statistics

Recommended, big picture:
• A. C. Davison and D. V. Hinkley, Bootstrap Methods and their Applications
• Bradley Efron
  • "Bootstrap Methods: Another Look at the Jackknife", Annals of Statistics 7 (1979): 1--26 [The original paper; staggeringly understandable]
  • The Bootstrap, the Jackknife, and Other Resampling Plans [1982 notes volume]

Recommended, close-ups:
• Peter Bühlmann, "Sieve Bootstrap with Variable Length Markov Chains for Stationary Categorical Time Series", Journal of the American Statistical Association 97 (2002): 443--456 [PDF preprint]
• Paul Doukhan, Silika Prohl, and Christian Y. Robert, "Subsampling weakly dependent time series and application to extremes" [Thanks to Dr. Prohl for a pre-print]
• Silvia Goncalves and Halbert White, "Maximum likelihood and the bootstrap for nonlinear dynamic models", Journal of Econometrics 119 (2004): 199--219
• Hans R. Künsch, "The Jackknife and the Bootstrap for General Stationary Observations", Annals of Statistics 17 (1989): 1217--1241
• S. N. Lahiri, Resampling Methods for Dependent Data
• Elizaveta Levina and Peter J. Bickel, "Texture synthesis and nonparametric resampling of random fields", Annals of Statistics 34 (2006): 1751--1773

Modesty forbids me to recommend:
• CRS, "The Bootstrap", American Scientist 98 (2010): 186--190 [Self-commentary]

To read:
• Sylvain Arlot, Gilles Blanchard, and Etienne Roquain, "Some nonasymptotic results on resampling in high dimension, I: Confidence regions", Annals of Statistics 38 (2010): 51--82
• Peter Bühlmann, "Bootstraps for Time Series", Statistical Science 17 (2002): 52--72
• Snigdhansu Chatterjee and Arup Bose, "Generalized bootstrap for estimating equations", math.ST/0504515 = Annals of Statistics 33 (2005): 414--436
• Guang Cheng and Jianhua Z. Huang, "Bootstrap consistency for general semiparametric M-estimation", Annals of Statistics 38 (2010): 2884--2915
• Michael R. Chernick, Bootstrap Methods: A Practitioner's Guide
• Herold Dehling, Martin Wendler, "Central Limit Theorem and the Bootstrap for U-Statistics of Strongly Mixing Data", arxiv:0811.1888
• Efron and Tibshirani, An Introduction to the Bootstrap
• Yanqin Fan, Qi Li and Insik Min, "A Nonparametric Bootstrap Test of Conditional Distributions", Econometric Theoy 22 (2006): 587--613
• Jurgen Franke, Jens-Peter Kreiss and Enno Mammen, "Bootstrap of Kernel Smoothing in Nonlinear Time Series", Bernoulli 8 (2002): 1--37
• Philip Good
  • Permutation, Parametric, and Bootstrap Tests of Hypotheses
  • Resampling Methods: A Practical Guide to Data Analysis
• Peter G. Hall, The Bootstrap and Edgeworth Expansion
• Stephen M. S. Lee and P. Y. Lai, "Improving coverage accuracy of block bootstrap confidence intervals", arxiv:0804.4361
• Daniel J. Nordman, "A note on the stationary bootstrap's variance", Annals of Statistics 37 (2009): 359--370, arxiv:0903.0474
• Dimitris N. Politis, "The Impact of Bootstrap Methods on Time Series Analysis", Statistical Science 18 (2003): 219--230
• Dimitris N. Politis, Joseph P. Romano and Michael Wolf, Subsampling
• Zacharias Psaradakis
  • "A sieve bootstrap test for stationarity," Statistics and Probability Letters 62 (2003): 263--274
  • "Blockwise bootstrap testing for stationarity", Statistics and Probability Letters 76 (2006): 562--570
• Matias Salibian-Barrera, Stefan van Aelst and Gert Willems, "Fast and robust bootstrap", Statistical Methods and Applications 17 (2009): 41--71
• Jun Shao and Dongsheng Tu, The Jackknife and the Bootstrap
• Xiaofeng Shao, "The Dependent Wild Bootstrap", Journal of the American Statistical Association 105 (2010): 218--235
• Olimjon Sh. Sharipov and Martin Wendler, "Bootstrap for the Sample Mean and for U-Statistics of Stationary Processes", arxiv:0911.3083
• Herwig Wendt, Patrice Abry and Stephane Jaffard, "Bootstrap for Empirical Multifractal Analysis", IEEE Signal Processing Magazine July 2007, pp. 38--48 [+ technical papers by these authors]
• Abdelhak M. Zoubir and D. Robert Iskander, Bootstrap Techniques for Signal Processing