We deal with distributed estimation of deterministic vector parameters using ad hoc wireless sensor networks (WSNs). We cast the decentralized estimation problem as the solution of multiple convex optimization subproblems. Using the method of alternating multipliers we derive algorithms which are decomposable into a set of simpler tasks suitable for distributed implementation. Different from existing alternatives, our approach does not require knowing the desired estimator in closed-form thus allowing for distributed nonlinear estimation. Our algorithms have guaranteed convergence under ideal channel links, while they exhibit noise resilience provably established for the distributed best linear unbiased estimator (BLUE).