2020/09/09 by Ery Arias-Castro, Arias-Castro, Ery, Zheng, Lin
Decision Sciences · Engineering · Mathematics · #Control Systems and Identification #FOS: Electrical engineering #FOS: Mathematics #Optimal Experimental Design Methods #Signal Processing (eess.SP) #Statistical Methods and Inference #Statistics Theory (math.ST) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2009.04072
openalex publication_date 2020/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.