Detecting a Smooth Signal: Optimality of Cusum Based Procedures
该研究证明，在随机平滑函数模型下，基于残差累积和序列的统计量是对非多项式信号进行局部最优检验的方法，从理论上证实了残差累积和序列在检测平滑信号中的有效性。
Cox et al. (1988) show that under a random smooth function model with signal covariance matrix V, a locally most powerful test for the presence of a nonpolynomial signal is based on the statistic yTVy. We show that if a well-known difference-based roughness measure is used to derive a natural choice for V then this statistic is the sum of squares of a residual cusum sequence. Thus we confirm theoretically the long-held impression that the residual cusum sequence is powerful as a tool for the detection of smooth signal.