论文标题
部分可观测时空混沌系统的无模型预测
An Adaptively Resized Parametric Bootstrap for Inference in High-dimensional Generalized Linear Models
论文作者
论文摘要
当参数数量与样本量之间的比率不可忽略时，逻辑回归模型中的准确统计推断仍然是一个关键的挑战。这是因为基于经典渐近理论或自举计算的近似值大大降低了标记。本文介绍了一种调整大小的引导方法，以在任意维度中推断模型参数。与参数bootstrap一样，我们从分布中重新采样观察结果，该分布取决于估计的回归系数序列。新颖的是，该估计值实际上远非最大似然估计（MLE）。最近的理论研究MLE在高维度上的特性为此提供了信息，并通过适当地缩小MLE向原点收缩而获得。我们证明了调整大小的引导方法在模拟和真实数据示例中都产生有效的置信区间。我们的方法扩展到其他高维广义线性模型。
Accurate statistical inference in logistic regression models remains a critical challenge when the ratio between the number of parameters and sample size is not negligible. This is because approximations based on either classical asymptotic theory or bootstrap calculations are grossly off the mark. This paper introduces a resized bootstrap method to infer model parameters in arbitrary dimensions. As in the parametric bootstrap, we resample observations from a distribution, which depends on an estimated regression coefficient sequence. The novelty is that this estimate is actually far from the maximum likelihood estimate (MLE). This estimate is informed by recent theory studying properties of the MLE in high dimensions, and is obtained by appropriately shrinking the MLE towards the origin. We demonstrate that the resized bootstrap method yields valid confidence intervals in both simulated and real data examples. Our methods extend to other high-dimensional generalized linear models.
