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In this paper, we consider distributed linear least squares (LLS) and Bayesian minimum mean square error (BMMSE) parameter estimation over sensor networks. In particular, we propose distributed iterative algorithms that asymptotically converge to the centralized solutions. These algorithms are first studied for the case of unclustered (flat architecture) sensor networks; in this venue, we provide necessary and sufficient conditions for the distributed algorithm to converge. Subsequently, we extend our analysis to clustered sensor networks with pulsed inter-cluster updates. In this latter scenario, inter-cluster communications occur every Ã time steps (with Ã > 1) and the corresponding updates are held until the next update instant. Depending on sensor locations and the employed network topology construction algorithm, it may be the case that inter-cluster communications require higher transmitter power support than intracluster communications. For energy-constrained sensor networks, it will therefore be beneficial-from a power efficiency (or alternately, network lifetime) point of view-to limit the extent of inter-cluster communication, without significantly deteriorating the convergence properties of the distributed estimation algorithm. We anticipate that a pulsed inter-cluster update scheme will also be useful for applications such as ground or airborne sensor networks, where low probability of detection and interception is essential. Our analysis provides sufficient conditions under which such distributed estimation algorithms, operating on a pulsed inter-cluster update scheme, converge. Simulation results illustrating the dependence of the convergence rate of the algorithm on the hold interval Ã conclude the paper.