In this paper,we consider the problem of distributed signal processing in wireless sensor networks in imperfect environments.Inwireless sensor network,distortions are usually caused by sensor noise,quantization noise and channel effect.While statisticalsignal processing techniques have been considered for these distortions separately,an effective approach that can deal with thesethree major sources of errors is still lacking.And most of these approaches require the prior knowledge of probability densityfunction which may not be practical.A novel statistical model is presented here to quantify these errors in wireless sensor networks.The proposed approach is probability density function unaware and hence is also considered as auniversal estimator.The proposedmethod is applied to the data fusion and power scheduling problems in wireless sensor networks.Analytical bounds are alsoobtained.Results show that the proposed approach outperforms the conventional distributed estimation techniques and power scheduling methods in the literature.