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A frequentist asymptotic expansion method for error estimation is employedfor a network of gravitational wave detectors to assess the amount ofinformation that can be extracted from gravitational wave observations.Mathematically we derive lower bounds in the errors that any parameterestimator will have in the absence of prior knowledge to distinguish betweenthe post-Einsteinian (ppE) description of coalescing binary systems and that ofgeneral relativity. When such errors are smaller than the parameter value,there is possibility to detect these violations from GR. A parameter space withinclusion of dominant dephasing ppE parameters $(\beta, b)$ is used for a studyof first- and second-order (co)variance expansions, focusing on the inspiralstage of a nonspinning binary system of zero eccentricity detectible throughAdv. LIGO and Adv. Virgo. Our procedure is an improvement of the Cram\'{e}r-RaoLower Bound. When Bayesian errors are lower than our bound it means that theydepend critically on the priors. The analysis indicates the possibility ofconstraining deviations from GR in inspiral SNR ($\rho \sim 15-17$) regimesthat are achievable in upcoming scientific runs (GW150914 had an inspiral SNR$\sim 12$). The errors on $\beta$ also increase errors of other parameters suchas the chirp mass $\mathcal{M}$ and symmetric mass ratio $\eta$. Application isdone to existing alternative theories of gravity, which include modifieddispersion relation of the waveform, non-spinning models of quadratic modifiedgravity, and dipole gravitational radiation (i.e., Brans-Dicke type)modifications.

Measuring violations of General Relativity from single gravitational wave detection by non-spinning binary systems: higher-order asymptotic analysis