固定格点设计下加性单调模型的统计推断
Statistical Inference for Additive Monotone Models under the Fixed Lattice Design
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中文总结 AI 辅助
针对固定格点设计下的加性单调模型，建立了最小二乘估计量的联合极限分布，证明分量渐近独立，并构造了无需调参的置信区间，同时揭示了临界增长速度下的非枢轴性。
中文摘要 AI 辅助
我们研究了在一般固定格点设计下，加性单调模型中最小二乘估计量（LSEs）的统计推断。我们建立了这些估计量的联合极限分布，并表明不同加性分量的估计量是渐近独立的。每个分量极限分布的形式由相应坐标方向上设计点数量相对于总样本量 n 的增长速度决定。除了这一增长速度外，极限仅依赖于噪声水平，并且在非高斯情形下，还依赖于该分量的局部导数。特别地，该极限不依赖于模型的维数。当某一坐标方向上的设计点数量增长速度超过 n^(1/3) 时，我们基于枢轴极限分布构造了无需调参的点态置信区间，并通过数值模拟验证了该理论。我们进一步表明，在临界增长速度 n^(1/3) 下，这些区间所依赖的块大小归一化不再是枢轴的。我们还证明了一个具有独立价值的切换引理，它简化了保序回归中极限分布的推导。
英文摘要
We study statistical inference for least squares estimators (LSEs) in additive monotone models under a general fixed lattice design. We establish joint limiting distributions for the LSEs and show that the estimators of different additive components are asymptotically independent. The form of the limiting distribution of each component is determined by how fast the number of design points along the corresponding coordinate grows relative to the total sample size n. Apart from this growth rate, the limit depends only on the noise level and, in the non-Gaussian regimes, on the local derivative of the component. In particular, the limit does not depend on the dimension of the model. When the number of design points along a coordinate grows faster than n^(1/3), we construct tuning-free pointwise confidence intervals based on a pivotal limiting distribution, and we validate the theory in numerical simulations. We further show that the block-size normalization underlying these intervals fails to be pivotal at the critical growth rate n^(1/3). We also prove a switching lemma, of independent interest, that simplifies the derivation of limiting distributions in isotonic regression.
发表机构
- Rutgers, the State University of New Jersey（新泽西州立罗格斯大学）
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