  The local escape velocity provides valuable inputs to the mass profile of the
Galaxy, and requires understanding the tail of the stellar speed distribution.
Following Leonard $\&$ Tremaine (1990), various works have since modeled the
tail of the stellar speed distribution as $\propto (v_{\rm{esc}} -v)^k$, where
$v_{\rm{esc}}$ is the escape velocity, and $k$ is the slope of the
distribution. In such studies, however, these two parameters were found to be
largely degenerate and often a narrow prior is imposed on $k$ in order to
constrain $v_{\rm{esc}}$. Furthermore, the validity of the power law form is
likely to break down in the presence of multiple kinematic substructures. In
this paper, we introduce a strategy that for the first time takes into account
the presence of kinematic substructure. We model the tail of the velocity
distribution as a sum of multiple power laws without imposing strong priors.
Using mock data, we show the robustness of this method in the presence of
kinematic structure that is similar to the recently-discovered Gaia Sausage. In
a companion paper, we present the new measurement of the escape velocity and
subsequently the mass of the Milky Way using Gaia DR2 data.
