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This work deals with distributed estimation problem in hierarchical wireless sensor networks, where the network is divided into spatially disjoint groups called clusters. The sensors in each cluster observe a separate random source which is correlated with the sources being observed by other clusters. Each cluster has its designated cluster head (CH). The sensors in the clusters forward their observations to the CHs, which in turn communicate with a fusion center (FC). The estimation at the CHs and the FC is done based on the minimum mean square error estimation rule. To minimize the overall estimation distortion, we propose a power scheduling scheme that allocates power to the individual sensors and the CHs subject to constraints on the transmit power of individual clusters and the overall network. The correlation among the underlying sources leads to coupling of the optimization variables and the power allocation solution requires centralized computation, which may be computationally expensive. To this end, we propose an alternative formulation based on an upper-bound on the distortion function, which leads to a solution that exhibits favorable characteristics for distributed implementation. Simulation examples corroborate effectiveness of the proposed power scheduling scheme.