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Summary: Submitted to the Annals of Statistics
arXiv: math.PR/0000000
MULTIPLE TESTING OF LOCAL MAXIMA FOR
DETECTION OF PEAKS IN 1D
By Armin Schwartzman , Yulia Gavrilov and Robert J.
Adler
Dept. of Biostatistics, Harvard School of Public Health, and
Dept. of Electrical Engineering, Technion - Israel Institute of Technology
A topological multiple testing scheme for one-dimensional do-
mains is proposed where, rather than testing every spatial or tempo-
ral location for the presence of a signal, tests are performed only at
the local maxima of the smoothed observed sequence. Assuming uni-
modal true peaks with finite support and Gaussian stationary ergodic
noise, it is shown that the algorithm with Bonferroni or Benjamini-
Hochberg correction provides asymptotic strong control of the family
wise error rate and false discovery rate, and is power consistent, as the
search space and the signal strength get large, where the search space
may grow exponentially faster than the signal strength. Simulations
show that error levels are maintained for non-asymptotic conditions,
and that power is maximized when the smoothing kernel is close in
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