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Sensing and aggregation of noisy observations should not be considered asseparate issues. The quality of collective estimation involves a difficulttradeoff between sensing quality which increases by increasing the number ofsensors, and aggregation quality which typically decreases if the number ofsensors is too large. We examine a strategy for optimal aggregation for anensemble of independent sensors with constrained system capacity. We show thatin the large capacity limit larger scale aggregation always outperforms smallerscale aggregation at higher noise levels, while below a critical value ofnoise, there exist moderate scale aggregation levels at which optimalestimation is realized.

A Large Deviations Result for Aggregation of Independent Noisy Observations