Multi-Scale CUSUM Tests for Time Dependent Spherical Random Fields
研究了球面随机场在谐波域的结构断点检验渐近行为，证明了CUSUM检验的一致性，并应用于全球温度数据，发现气候变化影响不同尺度的空间波动。
This paper investigates the asymptotic behavior of structural break tests in the harmonic domain for time dependent spherical random fields. In particular, we prove a functional central limit theorem result for the fluctuations over time of the sample spherical harmonic coefficients, under the null of isotropy and stationarity; furthermore, we prove consistency of the corresponding CUSUM test, under a broad range of alternatives, including deterministic trend, abrupt change, and a nontrivial power alternative. Our results are then applied to NCEP data on global temperature: our estimates suggest that Climate Change does not simply affect global average temperatures, but also the nature of spatial fluctuations at different scales.