Application of asymptotic expansions for maximum likelihood estimators errors to gravitational waves from binary mergers: The single interferometer case

Journal Article · Tue Jun 15 04:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.81.124048· OSTI ID:21413232

Zanolin, M ^[1]; Vitale, S ^[1]; Makris, N ^[2]

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1. Embry-Riddle Aeronautical University, 3700 Willow Creek Road, Prescott, Arizona, 86301 (United States)
2. Massachusetts Institute of Technology, 77 Mass Ave, Cambridge, Massachusetts, 02139 (United States)

In this paper we apply to gravitational waves (GW) from the inspiral phase of binary systems a recently derived frequentist methodology to calculate analytically the error for a maximum likelihood estimate of physical parameters. We use expansions of the covariance and the bias of a maximum likelihood estimate in terms of inverse powers of the signal-to-noise ration (SNR)s where the square root of the first order in the covariance expansion is the Cramer Rao lower bound (CRLB). We evaluate the expansions, for the first time, for GW signals in noises of GW interferometers. The examples are limited to a single, optimally oriented, interferometer. We also compare the error estimates using the first two orders of the expansions with existing numerical Monte Carlo simulations. The first two orders of the covariance allow us to get error predictions closer to what is observed in numerical simulations than the CRLB. The methodology also predicts a necessary SNR to approximate the error with the CRLB and provides new insight on the relationship between waveform properties, SNR, dimension of the parameter space and estimation errors. For example the timing match filtering can achieve the CRLB only if the SNR is larger than the Kurtosis of the gravitational wave spectrum and the necessary SNR is much larger if other physical parameters are also unknown.

• OSTI ID: 21413232
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 12 Vol. 81; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
79 ASTRONOMY AND ASTROPHYSICS
APPROXIMATIONS
ASYMPTOTIC SOLUTIONS
CALCULATION METHODS
COMPARATIVE EVALUATIONS
COMPUTERIZED SIMULATION
DISTRIBUTION
EVALUATION
EXPANSION
FORECASTING
GRAVITATIONAL WAVES
INTERFEROMETERS
MATHEMATICAL SOLUTIONS
MAXIMUM-LIKELIHOOD FIT
MEASURING INSTRUMENTS
MONTE CARLO METHOD
NOISE
NUMERICAL SOLUTION
SIMULATION
SPECTRA
WAVE FORMS