Modelling the COVID-19 Infection Trajectory: A Piecewise Linear Quantile Trend Model
提出分段线性分位数趋势模型，同时分析多个分位点上的COVID-19每日新增病例曲线，稳健处理异常值和异方差性，自动给出点预测和区间预测，并用于35个国家的感染曲线分析及短期预测。
Abstract We propose a piecewise linear quantile trend model to analyse the trajectory of the COVID-19 daily new cases (i.e. the infection curve) simultaneously across multiple quantiles. The model is intuitive, interpretable and naturally captures the phase transitions of the epidemic growth rate via change-points. Unlike the mean trend model and least squares estimation, our quantile-based approach is robust to outliers, captures heteroscedasticity (commonly exhibited by COVID-19 infection curves) and automatically delivers both point and interval forecasts with minimal assumptions. Building on a self-normalized (SN) test statistic, this paper proposes a novel segmentation algorithm for multiple change-point estimation. Theoretical guarantees such as segmentation consistency are established under mild and verifiable assumptions. Using the proposed method, we analyse the COVID-19 infection curves in 35 major countries and discover patterns with potentially relevant implications for effectiveness of the pandemic responses by different countries. A simple change-adaptive two-stage forecasting scheme is further designed to generate short-term prediction of COVID-19 cumulative new cases and is shown to deliver accurate forecast valuable to public health decision-making.