Distributed estimation of random parameter vector is dealt with using ad hoc wireless sensor networks (WSNs). The decentralized estimation problem is cast as the solution of multiple convex optimization subproblems and the alternating direction method of multipliers is employed to derive algorithms which can be decomposed into a set of simpler tasks suitable for distributed implementation. Different from existing alternatives, the novel approach does not require knowing the desired estimator in closed-form as is generally the case with the maximum a posteriori estimator (MAP). In addition, a priori information is accounted for and sensor observations are allowed to be correlated. The resulting algorithms converge to the centralized estimators under ideal channel links, while they exhibit noise robustness provably established for the distributed linear minimum mean-square error estimator (LMMSE).