发表机构
The Chinese University of Hong Kong（香港中文大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种适用于重复测量的新高阶偏差校正差分方差估计方法，通过交错组间与组内差分，在有限样本和高信噪比下表现优异。
AI 中文摘要
本文提出了一个通用的差分框架，用于在多种设置下进行方差估计。我们证明，在具有重复测量的非参数回归中，传统的基于差分的噪声方差估计量无法达到所需的偏差校正能力。通过交错组间差分和组内差分，我们提出了一种适用于重复测量的新高阶偏差校正差分方案。我们研究了新序列和估计量的理论性质。我们的方法在有限样本和高信噪比场景下特别有效，因为这些场景中渐近收敛尚未完全发挥作用，而我们的方法具有强大的偏差校正能力。
英文摘要
In this paper, we formulate a general differencing framework for variance estimation across a range of settings. We demonstrate that conventional difference-based noise variance estimators cannot achieve the desired bias-correcting power in nonparametric regression with repeated measurements. A new high-order bias-corrected differencing scheme, adapted to repeated measurements, is proposed by interlacing inter-group and intra-group differencing. The theoretical properties of the new sequences and estimators are studied. Our proposals are particularly efficient in finite samples and under high signal-to-noise ratio scenarios, where asymptotic convergence has not yet fully taken effect, due to their strong bias-correcting power.
