基于M-估计的模板匹配和变点检测
Template Matching and Change Point Detection by M-estimation
摘要：
我们考虑的基本问题匹配的模板信号。我们通过M估计来这样做，M估计包括对疏失误差具有鲁棒性的程序（即，离群值）。利用经验过程理论的标准结果，在相对较弱的假设下，我们得到了M-估计的收敛速度和渐近分布.我们还讨论了估计的最优性，无论是在有限样本的极大极小意义下，并在大样本限制的局部极大极小和相对效率。虽然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的移位模型，但我们在论文的最后考虑了许多扩展，包括更灵活的模板，固定设计，不可知论设置等等。
英文摘要：
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.
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