Randomization Inference of Periodicity in Unequally Spaced Time Series with Application to Exoplanet Detection
不等间隔时间序列周期性的随机化推断及系外行星探测应用AI 解读 ↓
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不等间隔时间序列周期性的随机化推断及系外行星探测应用
- 研究问题
- 观测时点不等间隔且具有确定性周期模式时，如何区分真实周期与观测安排诱发的干扰周期，并构造可靠的周期置信集合？
- 方法与思路
- 作者结合随机化推断与部分识别，对候选周期构造检验并反演为置信集合，同时提出减轻计算负担的近似实现及改进观测设计。
- 材料陈述的贡献
- 摘要称完整实现具有有限样本有效性、近似实现可具有渐近有效性，并在径向速度应用中识别已确认行星周期及部分未确认信号的弱证据。
- 阅读关注点
- 应核对随机化机制、检验有效性的假设、干扰周期的处理方式，以及近似计算条件和观测设计随机化如何改善识别。
- 阅读边界
- 这是 arXiv 预印本，不能据此认定已同行评审或期刊接收；摘要未说明检验的完整条件与计算成本，有效性不能理解为无条件保证。
原文摘要
The estimation of periodicity is a fundamental task in many scientific areas of study. Existing methods rely on theoretical assumptions that the observation times have equal or i.i.d. spacings, and that common estimators, such as the periodogram peak, are consistent and asymptotically normal. In practice, however, these assumptions are unrealistic as observation times usually exhibit deterministic patterns -- e.g., the nightly observation cycle in astronomy -- that imprint nuisance periodicities in the data. These nuisance signals also affect the finite-sample distribution of estimators, which can substantially deviate from normality. Here, we propose a set identification method, fusing ideas from randomization inference and partial identification. In particular, we develop a sharp test for any periodicity value, and then invert the test to build a confidence set. This approach is appropriate here because the construction of confidence sets does not rely on assumptions of regular or well-behaved asymptotics. Notably, our inference is valid in finite samples when our method is fully implemented, while it can be asymptotically valid under an approximate implementation designed to ease computation. Empirically, we validate our method in exoplanet detection using radial velocity data. In this context, our method correctly identifies the periodicity of the confirmed exoplanets in our sample. For some other, yet unconfirmed detections, we show that the statistical evidence is weak, which illustrates the failure of traditional statistical techniques. Last but not least, our method offers a constructive way to resolve these identification issues via improved observation designs. In exoplanet detection, these designs suggest meaningful improvements in identifying periodicity even when a moderate amount of randomization is introduced in scheduling radial velocity measurements.