  Gravitational wave observations have great potential to reveal new
information about the fundamental nature of gravity, but extracting that
information can be difficult. One popular technique is the parametrized
inspiral test of general relativity (a realization of the parametrized
post-Einsteinian framework), where the gravitational waveform, as calculated in
Einstein's theory as a series expansion in the orbital velocity, is
parametrically deformed at a given set of orders in velocity. However, most
current approaches usually only analyze the data while considering a single,
specific modification at a time. Are then constraints placed with a single
modification robust to our ignorance of higher post-Newtonian order
corrections? We show here that for a wide class of theories, specifically those
that admit a post-Newtonian expansion, single-parameter tests are indeed
robust. In particular, through a series of full Bayesian parameter estimation
studies on several different sets of synthetic data, we show that
single-parameter constraints are not degraded but rather are improved by the
inclusion of multiple parameters, provided one includes information about the
mathematical structure of the series. We then exemplify this with a specific
theory of gravity, shift-symmetric scalar Gauss-Bonnet theory, where the
waveform has been calculated to higher post-Newtonian orders than leading. We
show that the inclusion of these higher order terms strengthens
single-parameter constraints, instead of weakening them, and that the
strengthening is very mild. This analysis therefore provides strong evidence
that single-parameter post-Einsteinian tests of general relativity are robust
to ignorance of high post-Newtonian order terms in the general relativistic
deformations.
