Adaptive Multiscale Detection of Filamentary Structures Embedded in a Background of Uniform Random Points

@inproceedings{AriasCastro2003AdaptiveMD,
  title={Adaptive Multiscale Detection of Filamentary Structures Embedded in a Background of Uniform Random Points},
  author={Ery Arias-Castro and David L. Donoho and Xuan Huo and June},
  year={2003}
}
We are given a set of n points that appears uniformly distributed in the unit square [0, 1]. We wish to test whether the set actually is generated from a non-uniform distribution having a small fraction of points concentrated on some (a priori unknown) curve with C-norm bounded by β. An asymptotic detection threshold exists in this problem; for a constant T−(α, β) > 0, if the number of points on the curve is smaller than T−(α, β)n, reliable detection is not possible for large n. We describe a… CONTINUE READING
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