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We present an elementary mathematical method to find the minimax estimator of the Bernoulli proportion θ under the squared error loss when θ belongs to the restricted parameter space of the form Ω = [0, η] for some pre-specified constant 0 ≤ η ≤ 1. This problem is inspired from the problem of estimating the rate of positive COVID-19 tests. The presented results and applications would be useful materials for both instructors and students when teaching point estimation in statistical or machine learning courses.

We estimate the general influence functions for spatio-temporal Hawkes processes using a tensor recovery approach by formulating the location dependent influence function that captures the influence of historical events as a tensor kernel. We assume a low-rank structure for the tensor kernel and cast the estimation problem as a convex optimization problem using the Fourier transformed nuclear norm (TNN). We provide theoretical performance guarantees for our approach and present an algorithm to solve the optimization problem. We demonstrate the efficiency of our estimation with numerical simulations.