A Bias Bound Approach to Non-parametric Inference
非参数推断的偏差界方法AI 解读 ↓
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非参数推断的偏差界方法
- 研究问题
- 非参数估计采用均方误差最优带宽时，如何在偏差不可忽略的情况下构造有效区间，避免依赖欠平滑？
- 方法与思路
- 作者不直接一致估计点态偏差，而是估计偏差绝对值的上界，并将其纳入使用均方误差最优带宽的置信区间。
- 材料陈述的贡献
- 摘要称，在其所述基本假设下，偏差上界可被一致估计，从而得到有效且长度按最优速度缩短的置信区间。
- 阅读关注点
- 应核对偏差界的原始假设、可行估计方式、覆盖保证是点态还是一致，以及最优区间长度所针对的函数类别。
- 阅读边界
- 所给Crossref摘要未列出具体光滑性条件、区间公式或覆盖范围；不能将作者所称的最小假设理解为无条件有效。
原文摘要
Abstract The traditional approach to obtain valid confidence intervals for non-parametric quantities is to select a smoothing parameter such that the bias of the estimator is negligible relative to its standard deviation. While this approach is apparently simple, it has two drawbacks: first, the question of optimal bandwidth selection is no longer well-defined, as it is not clear what ratio of bias to standard deviation should be considered negligible. Second, since the bandwidth choice necessarily deviates from the optimal (mean squares-minimizing) bandwidth, such a confidence interval is very inefficient. To address these issues, we construct valid confidence intervals that account for the presence of a non-negligible bias and thus make it possible to perform inference with optimal mean squared error minimizing bandwidths. The key difficulty in achieving this involves finding a strict, yet feasible, bound on the bias of a non-parametric estimator. It is well-known that it is not possible to consistently estimate the pointwise bias of an optimal non-parametric estimator (for otherwise, one could subtract it and obtain a faster convergence rate violating Stone’s bounds on the optimal convergence rates). Nevertheless, we find that, under minimal primitive assumptions, it is possible to consistently estimate an upper bound on the magnitude of the bias, which is sufficient to deliver a valid confidence interval whose length decreases at the optimal rate and which does not contradict Stone’s results.