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Speeding Up Non-Parametric Bootstrap Computations for Statistics Based on Sample Moments in Small/Moderate Sample Size Applications.

ABSTRACT: In this paper we propose a vectorized implementation of the non-parametric bootstrap for statistics based on sample moments. Basically, we adopt the multinomial sampling formulation of the non-parametric bootstrap, and compute bootstrap replications of sample moment statistics by simply weighting the observed data according to multinomial counts instead of evaluating the statistic on a resampled version of the observed data. Using this formulation we can generate a matrix of bootstrap weights and compute the entire vector of bootstrap replications with a few matrix multiplications. Vectorization is particularly important for matrix-oriented programming languages such as R, where matrix/vector calculations tend to be faster than scalar operations implemented in a loop. We illustrate the application of the vectorized implementation in real and simulated data sets, when bootstrapping Pearson's sample correlation coefficient, and compared its performance against two state-of-the-art R implementations of the non-parametric bootstrap, as well as a straightforward one based on a for loop. Our investigations spanned varying sample sizes and number of bootstrap replications. The vectorized bootstrap compared favorably against the state-of-the-art implementations in all cases tested, and was remarkably/considerably faster for small/moderate sample sizes. The same results were observed in the comparison with the straightforward implementation, except for large sample sizes, where the vectorized bootstrap was slightly slower than the straightforward implementation due to increased time expenditures in the generation of weight matrices via multinomial sampling.

SUBMITTER: Chaibub Neto E

PROVIDER: S-EPMC4488363 | biostudies-literature | 2015

REPOSITORIES: biostudies-literature

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Speeding Up Non-Parametric Bootstrap Computations for Statistics Based on Sample Moments in Small/Moderate Sample Size Applications.

Chaibub Neto Elias E

PloS one 20150630 6

In this paper we propose a vectorized implementation of the non-parametric bootstrap for statistics based on sample moments. Basically, we adopt the multinomial sampling formulation of the non-parametric bootstrap, and compute bootstrap replications of sample moment statistics by simply weighting the observed data according to multinomial counts instead of evaluating the statistic on a resampled version of the observed data. Using this formulation we can generate a matrix of bootstrap weights an ...[more]

PMID: 26125965

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Project description:BackgroundAn appropriate sample size is essential for obtaining a precise and reliable outcome of a study. In machine learning (ML), studies with inadequate samples suffer from overfitting of data and have a lower probability of producing true effects, while the increment in sample size increases the accuracy of prediction but may not cause a significant change after a certain sample size. Existing statistical approaches using standardized mean difference, effect size, and statistical power for determining sample size are potentially biased due to miscalculations or lack of experimental details. This study aims to design criteria for evaluating sample size in ML studies. We examined the average and grand effect sizes and the performance of five ML methods using simulated datasets and three real datasets to derive the criteria for sample size. We systematically increase the sample size, starting from 16, by randomly sampling and examine the impact of sample size on classifiers' performance and both effect sizes. Tenfold cross-validation was used to quantify the accuracy.ResultsThe results demonstrate that the effect sizes and the classification accuracies increase while the variances in effect sizes shrink with the increment of samples when the datasets have a good discriminative power between two classes. By contrast, indeterminate datasets had poor effect sizes and classification accuracies, which did not improve by increasing sample size in both simulated and real datasets. A good dataset exhibited a significant difference in average and grand effect sizes. We derived two criteria based on the above findings to assess a decided sample size by combining the effect size and the ML accuracy. The sample size is considered suitable when it has appropriate effect sizes (≥ 0.5) and ML accuracy (≥ 80%). After an appropriate sample size, the increment in samples will not benefit as it will not significantly change the effect size and accuracy, thereby resulting in a good cost-benefit ratio.ConclusionWe believe that these practical criteria can be used as a reference for both the authors and editors to evaluate whether the selected sample size is adequate for a study.

Dataset Information

Speeding Up Non-Parametric Bootstrap Computations for Statistics Based on Sample Moments in Small/Moderate Sample Size Applications.

Publications

Speeding Up Non-Parametric Bootstrap Computations for Statistics Based on Sample Moments in Small/Moderate Sample Size Applications.

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