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