论文信息 - Bootstrapping data arrays of arbitrary order

Bootstrapping data arrays of arbitrary order

In this paper we study a bootstrap strategy for estimating the variance of a mean taken over large multifactor crossed random effects data sets. We apply bootstrap reweighting independently to the levels of each factor, giving each observation the product of independently sampled factor weights. No exact bootstrap exists for this problem [McCullagh (2000) Bernoulli 6 285-301]. We show that the proposed bootstrap is mildly conservative, meaning biased toward overestimating the variance, under sufficient conditions that allow very unbalanced and heteroscedastic inputs. Earlier results for a resampling bootstrap only apply to two factors and use multinomial weights that are poorly suited to online computation. The proposed reweighting approach can be implemented in parallel and online settings. The results for this method apply to any number of factors. The method is illustrated using a 3 factor data set of comment lengths from Facebook.

A. Owen | Dean Eckles

[1] P. J. McCarthy. PSEUDO-REPLICATION: HALF SAMPLES' , 1969 .

[2] D. Rubin. The Bayesian Bootstrap , 1981 .

[3] E. Mammen. When Does Bootstrap Work?: Asymptotic Results and Simulations , 1992 .

[4] P. Hall. The Bootstrap and Edgeworth Expansion , 1992 .

[5] E. Mammen. Bootstrap and Wild Bootstrap for High Dimensional Linear Models , 1993 .

[6] M. Newton. Approximate Bayesian-inference With the Weighted Likelihood Bootstrap , 1994 .

[7] Peter McCullagh,et al. Resampling and exchangeable arrays , 2000 .

[8] Karl J. Friston,et al. Variance Components , 2003 .

[9] Herbert K. H. Lee,et al. Lossless Online Bayesian Bagging , 2004, J. Mach. Learn. Res..

[10] Stuart J. Russell,et al. Online bagging and boosting , 2005, 2005 IEEE International Conference on Systems, Man and Cybernetics.

[11] James Bennett,et al. The Netflix Prize , 2007 .

[12] Art B. Owen,et al. THE PIGEONHOLE BOOTSTRAP , 2007, 0712.1111.

[13] David Hinkley,et al. Bootstrap Methods: Another Look at the Jackknife , 2008 .

[14] Pete Wyckoff,et al. Hive - A Warehousing Solution Over a Map-Reduce Framework , 2009, Proc. VLDB Endow..

[15] Bradley A. Hanson,et al. The Bootstrap and Other Procedures for Examining the Variability of Estimated Variance Components in Testing Contexts , 2014 .