L. Plaskota

How to benefit from noise.

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Abstract.   We compare nonadaptive and adaptive designs for estimating linear functionals in the minimax statistical setting. It is well known that adaptive designs do not lead to better approximations in the worst case setting for convex and symmetric a priori classes, and in the average case setting with Gaussian a priori distributions. However, it turns out that adaptive designs can be significantly better than nonadaptive ones in the statistical setting. Moreover, using adaptive designs one can obtain much better estimators for noisy data than for exact data. These results are possible, because the adaptive statistical setting with noisy data enables the Monte Carlo simulation.

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