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In this paper we describe a new methodology to calculate analytically theerror for a maximum likelihood estimate (MLE) for physical parameters fromGravitational wave signals. All the existing litterature focuses on the usageof the Cramer Rao Lower bounds (CRLB) as a mean to approximate the errors forlarge signal to noise ratios. We show here how the variance and the bias of aMLE estimate can be expressed instead in inverse powers of the signal to noiseratios where the first order in the variance expansion is the CRLB. As anapplication we compute the second order of the variance and bias for MLE ofphysical parameters from the inspiral phase of binary mergers and for noises ofgravitational wave interferometers . We also compare the improved errorestimate with existing numerical estimates. The value of the second order ofthe variance expansions allows to get error predictions closer to what isobserved in numerical simulations. It also predicts correctly the necessary SNRto approximate the error with the CRLB and provides new insight on therelationship between waveform properties SNR and estimation errors. For examplethe timing match filtering becomes optimal only if the SNR is larger than thekurtosis of the gravitational wave spectrum.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

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