RESAMPLING FEWER THAN n OBSERVATIONS: GAINS, LOSSES, AND REMEDIES FOR LOSSES

By Peter J. Bickel, Friedrich Götze, W. Zwet. 2012

353 citations recorded by the source corpus.

We discuss a number of resampling schemes in which m = o(n) observations are resampled. We review nonparametric bootstrap failure and give results old and new on how the m out of n with replacement and without replacement bootstraps work. We extend work of Bickel and Yahav (1988) to show that m out of n bootstraps can be made second order correct, if the usual nonparametric bootstrap is correct and study how these extrapolation techniques work when the nonparametric bootstrap does not.

Subfields: Finance, Statistics and Probability

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Citations in the corpus

Forward stability and model path selection (2021, neutral): “In deciding between bootstrapping and subsampling, note that by seeking to identify the most probable covariates to include, we are dealing with a discrete-valued parameter, which is known to be a common source of bootstrap failure (Bickel et al. 1997; Davison and Hink-ley 1999).”
Models as Approximations II: A Model-Free Theory of Parametric Regression (2016, methodology): “1 but could have been gleaned from Fisher consistency (4).”
Monte-Carlo based uncertainty analysis: Sampling efficiency and sampling convergence (2013, background): “For the study here, only five groups are applied for sample-splitting, while higher numbers are advocated in the literature [63,64].”
Belief Network Analysis: A Relational Approach to Understanding the Structure of Attitudes (2017, methodology): “Since including two copies of the same variable in one betweenness analysis would not yield meaningful results, we resampled the item set using an “m out of n” resampling scheme (Bickel, Götze, and Zwet 2012).”
Inference on Directionally Differentiable Functions (2014, methodology): “We refer to the functionals, we know by way of example that the consistency of the standard bootstrap may not (Bickel et al ., 1997; Andrews, 2000).”
Models as Approximations I: Consequences Illustrated with Linear Regression (2014, neutral): “According to (7) and (8), m2( ~ X) can be replaced by δ2 and σ2( ~ X) by 2: (17) E[m(2)( ~ X) ~ X ~ X ′ ] = E[ δ(2) ~ X ~ X ′ ], E[σ(2)( ~ X) ~ X ~ X ′ ] = E[ 2 ~ X ~ X ′ ].”
The Big Data Bootstrap (2012, methodology): “Efforts to ameliorate statistical shortcomings of the bootstrap in turn led to the development of related methods such as the m out of n bootstrap and subsampling (Bickel et al., 1997; Politis et al., 1999).”
Matching and semi-parametric IV estimation, a distance-based measure of migration, and the wages of young men (2011, methodology): “Politis and Romano (1994) and Bickel et al. (1997) show that when the bootstrap fails, using subampling or the ‘m out of n’ bootstrap usually rectifies this problem; i.e. one must assume relatively minimal regularity conditions24.”
Statistical Inference for Average Treatment Effects Estimated by Synthetic Control Methods (2019, methodology): “(2)Choosing a subsample size m out of the original T1 data with or without replacement are asymptotically equivalent under mild conditions including m/T1 → 0, m → ∞ as T1 → ∞, see Bickel et al. (1997). One advantage of using the ‘with replacement’ method is that, when bootstrap method works, the sub”
A scalable bootstrap for massive data (2011, methodology): “Another landmark in the development of simulation-based inference is subsampling (Poli-tis et al., 1999) and the closely related m out of n bootstrap (Bickel et al., 1997).”
A Sparse Singular Value Decomposition Method for High-Dimensional Data (2014, methodology): “This is the general problem of the “ m out of n ” bootstrap, which was examined by Bickel, Gotze, and Zwet (1997).”