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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 constrained convex optimization subproblems. Using the method of multipliers in conjunction with a block coordinate descent approach we demonstrate how the resultant algorithm can be decomposed into a set of simpler tasks suitable for distributed implementation. Different from existing alternatives, our approach does not require the centralized estimator to be expressible in a separable closed form in terms of averages, thus allowing for decentralized computation even of nonlinear estimators, including maximum likelihood estimators (MLE) in nonlinear and non-Gaussian data models. We prove that these algorithms have guaranteed convergence to the desired estimator when the sensor links are assumed ideal. Furthermore, our decentralized algorithms exhibit resilience in the presence of receiver and/or quantization noise. In particular, we introduce a decentralized scheme for least-squares and best linear unbiased estimation (BLUE) and establish its convergence in the presence of communication noise. Our algorithms also exhibit potential for higher convergence rate with respect to existing schemes. Corroborating simulations demonstrate the merits of the novel distributed estimation algorithms.