A Signal Extraction Approach to the Estimation of Treatment and Control Curves
提出一种信号提取方法，同时估计处理组和对照组的平均响应曲线及其变化率，并在干预时间点施加平滑过渡约束，适用于经济学或生物学中的干预效应分析。
Abstract Suppose that the response of a group of subjects, which we call the control group, is monitored over time. At a given time after the start of the experiment, the experimenter intervenes and applies a treatment to a subset of the group. We propose a signal extraction approach to the simultaneous estimation of the treatment and control mean response curves, and their rates of change, imposing a smooth transition constraint between the two curves at the time of intervention. By expressing the model in state-space form, we show how to compute the likelihood and the cross-validation function efficiently in O(n) operations together with the response curve estimates and their standard errors. We also show that the curve estimates are solutions to a penalized least squares problem. A small simulation study to assess the performance of the generalized cross-validation and marginal likelihood estimates of the smoothing parameter is carried out, and the methodology in the article is applied to an experiment on the growth of lupin when fertilizer is added to a subgroup of the plants 47 days after planting.