  The population of stellar-mass, compact object binaries that merge with
non-negligible eccentricity may be large enough to motivate searches with
ground-based gravitational wave detectors. Such events could be exceptional
laboratories to test General Relativity in the dynamical, strong-field regime,
as a larger fraction of the energy is emitted at high-velocities, compared to
quasi-circular inspirals. A serious obstacle here, however, is the challenge of
computing theoretical waveforms for eccentric systems with the requisite
accuracy for use in a matched-filter search. The corresponding waveforms are
more a sequence of concentrated bursts of energy emitted near periapse than a
continuous waveform. Based on this, an alternative approach, stacking excess
power over the set of time-frequency tiles coincident with the bursts, was
recently suggested as a more practical (though sub-optimal) detection strategy.
The leading-order "observable" that would be inferred from such a detection
would be a sequence of discrete numbers characterizing the position and size of
each time-frequency tile. In General Relativity, this (possibly large) sequence
of numbers is uniquely determined by the small set of parameters describing the
binary at formation. In this work, following the spirit of the parameterized
post-Einsteinian framework developed for quasi-circular inspiral, we propose a
simple, parameterized deformation of the baseline general relativistic burst
algorithm for eccentric inspiral events that would allow for model-independent
tests of Einstein's theory in this high-velocity, strong-field regime.
