Speeding Up Non-Parametric Bootstrap Computations for Statistics Based on Sample Moments in Small/Moderate Sample Size Applications.
Speeding Up Non-Parametric Bootstrap Computations for Statistics Based on Sample Moments in Small/Moderate Sample Size Applications.
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DOI：
10.1371/journal.pone.0131333
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发表时间：
2015
期刊：
影响因子：
3.7
通讯作者：
Chaibub Neto E
中科院分区：
文献类型：
--
作者：
Chaibub Neto E
本文提出了一种基于样本矩的非参数自举方法的向量化实现。基本上，我们采用非参数自助抽样的多项式抽样公式，并通过简单地根据多项式计数对观测数据进行加权来计算样本矩统计量的自助复制，而不是对观测数据的重新采样版本进行统计评估。使用这个公式，我们可以生成一个自举权重矩阵，并通过几个矩阵乘法来计算自举复制的整个向量。向量化对于面向矩阵的编程语言（如R）尤其重要，其中矩阵/向量计算往往比循环中实现的标量操作更快。我们说明了应用程序的向量化实现在真实的和模拟数据集，当引导皮尔逊的样本相关系数，并比较其性能对两个国家的最先进的R实现的非参数引导，以及一个简单的循环的基础上。我们的调查涵盖了不同的样本量和bootstrap重复次数。在所有测试的情况下，矢量化引导程序与最先进的实现相比都是有利的，并且对于小/中等样本量来说显着/相当快。在与直接实现的比较中观察到相同的结果，除了大样本量之外，其中向量化引导比直接实现稍慢，这是由于通过多项式采样生成权重矩阵的时间开销增加。
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.
影响因子：
4.5
作者：
RUBIN, DB
通讯作者：
RUBIN, DB
影响因子：
4.5
作者：
EFRON, B
通讯作者：
EFRON, B
影响因子：
6.1
作者：
Hanley, James A.;MacGibbon, Brenda
通讯作者：
MacGibbon, Brenda