In this paper, we advocate applying the concept of wake-up radio to distributed estimation in wireless sensor networks. With distributed estimation, where sensing data of multiple nodes are used for estimating a target observation, the energy consumption can be reduced by making only a subset of nodes in the network transmit their data, such that the collected data can guarantee the required estimation accuracy. In this case, a sink needs to selectively wake up sensor nodes whose data can contribute to the improvement of estimation accuracy. In this paper, we propose a wake-up signaling called estimative sampling (ES) that can realize the selective wake-up of desired nodes. The ES method includes a mechanism that dynamically searches the desired nodes over a distribution of sensing data. With numerical results obtained by computer simulations, we show that the distributed estimation with ES method achieves lower energy consumption than that with conventional identitybased wake-up while satisfying the required accuracy.