论文标题
模板匹配和更改点通过M估计检测
Template Matching and Change Point Detection by M-estimation
论文作者
论文摘要
我们考虑将模板与信号匹配的基本问题。我们通过m估计来做到这一点，其中包含对总错误（即离群值）强大的程序。利用经验过程理论的标准结果，我们得出了在相对温和的假设下M-静态器的收敛速率和渐近分布。我们还讨论了估计量的最佳性，无论是在最小值的有限样品中，都在局部最小值和相对效率方面以大样本限制进行了讨论。尽管本文的大部分内容都致力于在随机设计的背景下研究基本偏移模型，但我们考虑了本文结尾的许多扩展，包括更灵活的模板，固定设计，不可知论设置等。
We consider the fundamental problem of matching a template to a signal. We do so by M-estimation, which encompasses procedures that are robust to gross errors (i.e., outliers). Using standard results from empirical process theory, we derive the convergence rate and the asymptotic distribution of the M-estimator under relatively mild assumptions. We also discuss the optimality of the estimator, both in finite samples in the minimax sense and in the large-sample limit in terms of local minimaxity and relative efficiency. Although most of the paper is dedicated to the study of the basic shift model in the context of a random design, we consider many extensions towards the end of the paper, including more flexible templates, fixed designs, the agnostic setting, and more.
