Simultaneous Inference for Monotone and Smoothly Time-Varying Functions Under Complex Temporal Dynamics
复杂时间动态下单调且平滑时变函数的同时推断AI 解读 ↓
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复杂时间动态下单调且平滑时变函数的同时推断
- 研究问题
- 在具有复杂时间依赖的序列中，如何对单调平滑趋势及单调时变回归系数进行同时推断，并构造有效的置信带？
- 方法与思路
- 作者结合单调重排与非参数估计，利用高斯近似和专门设计的自助法构造同时置信带，分别处理多维趋势和时变系数模型。
- 材料陈述的贡献
- 摘要称，方法具有渐近有效性，模拟支持其表现，并用于多地区温度曲线和日照影响检验；单趋势比较中置信带较窄。
- 阅读关注点
- 应核对时间依赖、维度增长和单调性条件，以及自助法如何保持依赖结构、带宽选择与置信带覆盖率的评估。
- 阅读边界
- 依据所给 arXiv 预印本摘要，不能据此确认同行评审或期刊接收；未说明依赖条件及带宽规则，置信带较窄的陈述限于摘要所述比较。
原文摘要
We propose a new framework for the simultaneous inference of monotone and smoothly time-varying functions under complex temporal dynamics. This will be done utilizing the monotone rearrangement and the nonparametric estimation. We capitalize the Gaussian approximation for the nonparametric monotone estimator and construct the asymptotically correct simultaneous confidence bands (SCBs) using designed bootstrap methods. We investigate two general and practical scenarios. The first is the simultaneous inference of monotone smooth trends from moderately high-dimensional time series. The proposed algorithm has been employed for the joint inference of temperature curves from multiple areas. Specifically, most existing methods are designed for a single monotone smooth trend. In such cases, our proposed SCB empirically exhibits the narrowest width among existing approaches while maintaining confidence levels. It has also been used for testing several hypotheses tailored to global warming. The second scenario involves simultaneous inference of monotone and smoothly time-varying regression coefficients in time-varying coefficient linear models. The proposed algorithm has been utilized for testing the impact of sunshine duration on temperature which is believed to be increasing due to severe greenhouse effect. The validity of the proposed methods has been justified in theory as well as by extensive simulations.