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This paper describes the effect of channel estimation error (CEE) on the performance of distributed estimations of an unknown parameter in a wireless sensor network. Both the classical and Bayesian estimators are derived to mitigate the adverse effects caused by the CEE. Power scheduling among sensors and the power ratio between the training and data transmission at each individual node are optimized by directly minimizing the final average mean squared error to compensate for the CEE. A closed-form power scheduling policy is given for a homogeneous environment, which shows that more than 50% of the power should be allocated to sensor observation transmissions. For an inhomogeneous environment, a multilevel waterfilling type solution is developed for the power scheduling among sensors for only the sum power constraint with a “cave” waterfilling solution for both the sum and individual power constraints. Simulations show that the proposed power scheduling schemes achieve better performance than the equal power scheduling scheme.