On confidence intervals centered on bootstrap smoothed estimators
Paul Kabaila, Christeen Wijethunga
备注：
The abstract and introduction have been improved. Also, an outline of the proof of Theorem 1 has been taken from the Supplementary Material and added to the appendix. arXiv admin note: text overlap with arXiv:1610.09802
Bootstrap smoothed (bagged) estimators have been proposed as an improvement on estimators found after preliminary data-based model selection. Efron, 2014, derived a widely applicable formula for a delta method approximation to the standard deviation of the bootstrap smoothed estimator. He also considered a confidence interval centered on the bootstrap smoothed estimator, with width proportional to the estimate of this standard deviation. Kabaila and Wijethunga, 2019, assessed the performance of this confidence interval in the scenario of two nested linear regression models, the full model and a simpler model, for the case of known error variance and preliminary model selection using a hypothesis test. They found that the performance of this confidence interval was not substantially better than the usual confidence interval based on the full model, with the same minimum coverage. We extend this assessment to the case of unknown error variance by deriving a computationally convenient exact formula for the ideal (i.e. in the limit as the number of bootstrap replications diverges to infinity) delta method approximation to the standard deviation of the bootstrap smoothed estimator. Our results show that, unlike the known error variance case, there are circumstances in which this confidence interval has attractive properties.
Bootstrap smoothed (bagged) parameter estimators have been proposed as an improvement on estimators found after preliminary data-based model selection. The key result of Efron (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 (2014) proposed a confidence interval centered on the bootstrap smoothed estimator, with width proportional to the estimate of this approximation to the standard d…
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Online Inference in Distributional Temporal-Difference Learning
Yau Mathematical Sciences Center, Tsinghua University（清华大学丘成桐数学科学中心）；School of Statistics and Data Science, Shanghai University of Finance and Economics（上海财经大学统计与数据科学学院）
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