Consider a remote estimation problem where a sensor wants to communicate the state of an uncertain source to a remote estimator over a finite time horizon. The uncertain source is modeled as an autoregressive process with bounded noise. Given that the sensor has a limited communication budget, the sensor must decide when to transmit the state to the estimator who has to produce real-time estimates of the source state. In this paper, we consider the problem of finding a scheduling strategy for the sensor and an estimation strategy for the estimator to jointly minimize the worst-case maximum instantaneous estimation error over the time horizon. This leads to a decentralized minimax decision-making problem. We obtain a complete characterization of optimal strategies for this decentralized minimax problem. In particular, we show that an open loop communication scheduling strategy is optimal and the optimal estimate depends only on the most recently received sensor observation.