Template Matching and Change Point Detection by M-Estimation

We consider the fundamental problem of matching a template to signal. do so by M-estimation, which encompasses procedures that are robust gross errors (i.e., outliers). Using standard results from empirical process theory, we derive convergence rate and asymptotic distribution M-estimator under relatively mild assumptions. also discuss optimality estimator, both in finite samples minimax sense large-sample limit terms local minimaxity relative efficiency. Although most paper is dedicated study basic shift model context random design, many extensions towards end paper, including more flexible templates, fixed designs, agnostic setting, more.