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首页> 外文期刊>Australian & New Zealand journal of statistics >Confidence intervals centred on bootstrap smoothed estimators
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Confidence intervals centred on bootstrap smoothed estimators

机译：置信区间以bootstrap平滑估计量为中心

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Bootstrap smoothed (bagged) parameter estimators have been proposed as an improvement on estimators found after preliminary data-based model selection. A result of Efron in 2014 is a very convenient and widely applicable formula for a delta method approximation to the standard deviation of the bootstrap smoothed estimator. This approximation provides an easily computed guide to the accuracy of this estimator. In addition, Efron considered a confidence interval centred on the bootstrap smoothed estimator, with width proportional to the estimate of this approximation to the standard deviation. We evaluate this confidence interval in the scenario of two nested linear regression models, the full model and a simpler model, and a preliminary test of the null hypothesis that the simpler model is correct. We derive computationally convenient expressions for the ideal bootstrap smoothed estimator and the coverage probability and expected length of this confidence interval. In terms of coverage probability, this confidence interval outperforms the post-model-selection confidence interval with the same nominal coverage and based on the same preliminary test. We also compare the performance of the confidence interval centred on the bootstrap smoothed estimator, in terms of expected length, to the usual confidence interval, with the same minimum coverage probability, based on the full model.We comprehensively assess the performance of confidence intervals centred on the bootstrap smoothed estimator in the scenario of two nested linear regression models.
机译：已提出Bootstrap平滑（袋装）参数估计器，作为对基于初步数据的模型选择后发现的估计器的改进。埃夫隆（Efron）在2014年的研究结果是一个非常方便且可广泛应用的公式，用于将自举平滑估计器的标准差近似为增量法。这种近似为该估计器的精度提供了易于计算的指导。此外，埃夫隆（Efron）考虑了以自举平滑估计量为中心的置信区间，其宽度与对该近似值的估计值与标准偏差的估计值成比例。我们在两个嵌套的线性回归模型，完整模型和更简单的模型，以及对简单模型正确的零假设的初步检验的情况下，评估此置信区间。我们推导出理想的自举平滑估计器以及该置信区间的覆盖概率和预期长度的计算方便表达式。就覆盖率而言，在相同的名义覆盖率和基于相同的初步测试的情况下，该置信区间优于模型选择后的置信区间。我们还基于完整模型将以bootstrap平滑估计量为中心的置信区间的预期长度与具有相同最小覆盖概率的常规置信区间的预期长度进行了比较。在两个嵌套线性回归模型的情况下，使用自举平滑估计。

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