降雨模式的分布无关变点推断
Distribution-Free Changepoint Inference for Rainfall Patterns
AI总结：
针对降雨年内模式变点检测，提出分布无关框架，利用频谱特征与可交换性构建有限样本有效的变年置信集。
AI中文摘要：
长期的降雨记录包含关于一年内降水时间组织的关键信息，包括湿润期和干旱期。检测这种时间模式何时发生变化对于气候影响评估和环境监测至关重要。常见的数据结构包含来自m个地点在T年内的观测值。对于地点i和第t年，记录是一个日测量向量 $X_{i,t} = (X_{i,t,1},..., X_{i,t,D})^\top$，其中D=365。目标是识别一个未知的年份 $t_0$，在该年份区域内的降雨时间模式发生变化。由于年内模式的变化影响日序列的频域行为，我们通过一个频谱特征来表示每个年度曲线，该特征捕捉在固定频率下时间振荡的强度。许多变点方法依赖于参数似然或高斯近似，这对于偏斜和重尾的降雨数据难以证明其合理性。此外，许多程序仅返回点估计。在环境应用中，变年的置信集对于量化时间不确定性以及区分急剧转变与弱转变至关重要。本文开发了一个分布无关框架，用于检测独立监测地点间年度降雨模式的同步结构变化。对于每个地点-年份对，我们计算一个固定频率的非参数频谱密度估计。这些特征形成一个 $T \ imes m$ 数据矩阵。通过利用真实变点前后年度频谱特征的可交换性以及空间独立性，我们为未知变年构建了有限样本有效的置信集。
英文摘要：
Long records of rainfall contain critical information about the temporal organization of precipitation within a year, including wet and dry spells. Detecting when this temporal pattern changes is central to climate-impact assessment and environmental monitoring.A common data structure features observations from m locations over T years. For location i and year t, the record is a vector of daily measurements $X_{i,t} = (X_{i,t,1}, ..., X_{i,t,D})^\top$, with D = 365. The goal is to identify an unknown year $t_0$ when the temporal rainfall pattern changes across the region. Because changes in the intra-annual pattern affect the frequency-domain behavior of the daily sequence, we represent each yearly curve through a spectral feature capturing the strength of temporal oscillation at a fixed frequency.Classical changepoint methods often rely on parametric likelihoods or Gaussian approximations, which are hard to justify for skewed and heavy-tailed rainfall data. Furthermore, many procedures only return a point estimate. A confidence set for the change year is crucial in environmental applications to quantify temporal uncertainty and distinguish sharp transitions from weak evidence.This paper develops a distribution-free framework for detecting a synchronized structural change in yearly rainfall patterns across independently monitored locations. For each location-year pair, we compute a fixed-frequency nonparametric spectral density estimate. These features form a $T \times m$ data matrix. By exploiting the exchangeability of yearly spectral features before and after the true changepoint, alongside spatial independence, we construct finite-sample valid confidence sets for the unknown change year.
