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Authors: R P Croce, Th Demma, M Longo, S Marano, V Matta, V Pierro and I M Pinto

Ref: Class. Quantum Grav. 20 S803-S813 (2003)

Abstract: The cumulative distribution of the supremum of a set (bank) of correlators is investigated in the context of maximum likelihood detection of gravitational wave chirps from coalescing binaries with unknown parameters. Accurate (lower-bound) approximants are introduced based on a suitable generalization of previous results by Mohanty. Asymptotic properties (in the limit where the number of correlators goes to infinity) are highlighted. The validity of numerical simulations made on small-size banks is extended to banks of any size, via a Gaussian correlation inequality.

Notes: ‘The simplest assumption of statistical independence among N squared noncoherent correlators yields the CDF [1 - exp(-x)]ˆN for their supremum. Extensive numerical evidence [Dhurandhar and Schutz, Phys. Rev. D 50, 2390 (1994); Mohanty and Dhurandhar, Phys. Rev. D 54, 7108 (1996)] shows that this formula can be made fairly accurate provided N is reduced by a suitable factor epsilon, which can be loosely understood by assuming that all correlators in a covariance neighbourhood are counted as one [Jaranowski et al., Phys. Rev. D 58, 063001 (1998)]. An elegant argument whereby an approximate formula for epsilon could be obtained has been proposed by Mohanty [Phys. Rev. D 57, 630 (1998)], under the assumptions that (i) at most two (squared, noncoherent) correlators z, z' can simultaneously exceed a given threshold x, and (ii) these can only be nearest (largest absolute covariance) neighbours. Accurate (lower-bound) approximants are introduced based on a suitable generalization of previous results by Mohanty.’

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