For discrete perturbation sets between the hypercube and the odd integer grid, the focused width overestimates the detectability radius by at least a √(log n) factor in the Gaussian model and by n^{1/4} for Laplace data.
On com- binatorial testing problems.The Annals of Statistics, 38(5):3063–3092, 2010
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Focused Width in Adversarial Fake Detection: A Separation
For discrete perturbation sets between the hypercube and the odd integer grid, the focused width overestimates the detectability radius by at least a √(log n) factor in the Gaussian model and by n^{1/4} for Laplace data.