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February 2020 Multiple testing of local maxima for detection of peaks on the (celestial) sphere
Dan Cheng, Valentina Cammarota, Yabebal Fantaye, Domenico Marinucci, Armin Schwartzman
Bernoulli 26(1): 31-60 (February 2020). DOI: 10.3150/18-BEJ1068


We present a topological multiple testing scheme for detecting peaks on the sphere under isotropic Gaussian noise, where tests are performed at local maxima of the observed field filtered by the spherical needlet transform. Our setting is different from the standard Euclidean large domain asymptotic framework, yet highly relevant to realistic experimental circumstances for some important areas of application in astronomy, namely point-source detection in cosmic Microwave Background radiation (CMB) data. Motivated by this application, we shall focus on cases where a single realization of a smooth isotropic Gaussian random field on the sphere is observed, and a number of well-localized signals are superimposed on such background field. The proposed algorithms, combined with the Benjamini–Hochberg procedure for thresholding p-values, provide asymptotic control of the False Discovery Rate (FDR) and power consistency as the signal strength and the frequency of the needlet transform get large.


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Dan Cheng. Valentina Cammarota. Yabebal Fantaye. Domenico Marinucci. Armin Schwartzman. "Multiple testing of local maxima for detection of peaks on the (celestial) sphere." Bernoulli 26 (1) 31 - 60, February 2020.


Received: 1 May 2017; Revised: 1 June 2018; Published: February 2020
First available in Project Euclid: 26 November 2019

zbMATH: 07140492
MathSciNet: MR4036027
Digital Object Identifier: 10.3150/18-BEJ1068

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability


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Vol.26 • No. 1 • February 2020
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