We consider a power-constrained sensor network, consisting of multiple sensor nodes and a fusion center (FC), that is deployed for the purpose of estimating a common random parameter of interest. In contrast to the distributed framework, the sensor nodes are allowed to update their individual observations by (linearly) combining observations from neighboring nodes. The updated observations are communicated to the FC using an analog amplify-and-forward modulation scheme and through a coherent multiple access channel. The optimal collaborative strategy is obtained by minimizing the cumulative transmission power subject to a maximum distortion constraint. For the distributed scenario (i.e., with no observation sharing), the solution reduces to the power-allocation problem considered by Xiao et. al. . Collaboration among neighbors significantly improves power efficiency of the network in the low local-SNR regime, as demonstrated through an insightful example and numerical simulations.