论文标题
具有渐近条件有效性和无条件保证的自举预测间隔
Bootstrap prediction intervals with asymptotic conditional validity and unconditional guarantees
论文作者
论文摘要
可以说，最佳预测应考虑所有可用数据。因此，为了评估预测间隔的性能，应采用条件覆盖概率，以所有可用的观察为条件。为了关注线性模型，我们得出了标称预测间隔的条件覆盖概率与通过基于残差的引导程序获得的预测间隔的条件覆盖概率之间差异的渐近分布。在应用此结果时，我们表明，基于残留的自举产生的预测间隔约有50％的概率，可以产生条件覆盖的条件下。然后，我们开发了一种新的自举算法，该算法生成一个预测间隔，该预测间隔渐近地控制条件覆盖范围的概率以及条件覆盖不足的可能性。我们通过几个有限样本模拟补充了渐近结果。
It can be argued that optimal prediction should take into account all available data. Therefore, to evaluate a prediction interval's performance one should employ conditional coverage probability, conditioning on all available observations. Focusing on a linear model, we derive the asymptotic distribution of the difference between the conditional coverage probability of a nominal prediction interval and the conditional coverage probability of a prediction interval obtained via a residual-based bootstrap. Applying this result, we show that a prediction interval generated by the residual-based bootstrap has approximately 50% probability to yield conditional under-coverage. We then develop a new bootstrap algorithm that generates a prediction interval that asymptotically controls both the conditional coverage probability as well as the possibility of conditional under-coverage. We complement the asymptotic results with several finite-sample simulations.
