We consider the problem of link activation for distributed estimation with power constraint. To satisfy the requirement of power consumption, we propose a stochastic link activation scheme, where each sensor equipped with a distributed estimator sends data to its neighboring sensors according to different probabilities. First, we design the optimal estimator gain of each sensor to minimize the state estimation error covariance. Then, we find an upper bound of the expected state estimation error covariance and provide a sufficient condition to guarantee the stability of the proposed estimator. Finally, we formulate the link activation problem as an optimization problem, and convert it to a convex optimization. (C) 2016 Elsevier Ltd. All rights reserved.