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Article
Application of Asymptotic Expansions for Maximum Likelihood Estimators Errors to Gravitational Waves From Binary Mergers: The Single Interferometer Case
Physical Review D (2010)
  • M. Zanolin, Embry-Riddle Aeronautical University
  • S. Vitale, Universite Pierre-et-Marie-Curie
  • N. Makris, Massachusetts Institute of Technology
Abstract
In this paper we describe a new methodology to calculate analytically the error for a maximum likelihood estimate (MLE) for physical parameters from gravitational wave signals. All the existing literature focuses on the usage of the Cramer Rao Lower bounds (CRLB) as a mean to approximate the errors for large signal to noise ratios. We show here how the variance and the bias of an MLE estimate can be expressed instead in inverse powers of the signal to noise ratios where the first order in the variance expansion is the CRLB. As an application we compute the second order of the variance and bias for MLE of physical parameters from the inspiral phase of binary mergers and for noises of gravitational wave interferometers. We also compare the improved error estimate with existing numerical estimates. The value of the second order of the variance expansions allows to get error predictions closer to what is observed in numerical simulations. It also predicts correctly the necessary SNR to approximate the error with the CRLB and provides new insight on the relationship between waveform properties SNR and estimation errors. For example, the timing match filtering becomes optimal only if the SNR is larger than the kurtosis of the gravitational wave spectrum.
Keywords
  • coalescing binaries,
  • compact binaries,
  • parameters,
  • accuracy,
  • signals
Publication Date
June 25, 2010
DOI
https://doi.org/10.1103/PhysRevD.81.124048
Citation Information
M. Zanolin, S. Vitale and N. Makris. "Application of Asymptotic Expansions for Maximum Likelihood Estimators Errors to Gravitational Waves From Binary Mergers: The Single Interferometer Case" Physical Review D Vol. 81 Iss. 12 (2010) p. art. no. 124048 ISSN: 2470-0029
Available at: http://works.bepress.com/michele_zanolin/5/