  In this work we present a robust quantification of X-ray selected AGN in
local ($z \leq 0.25$) dwarf galaxies ($M_\mathrm{*} \leq 3 \times 10^9
\mathrm{M_\odot}$). We define a parent sample of 4,331 dwarf galaxies found
within the footprint of both the MPA-JHU galaxy catalogue (based on SDSS DR8)
and 3XMM DR7, performed a careful review of the data to remove
misidentifications and produced a sample of 61 dwarf galaxies that exhibit
nuclear X-ray activity indicative of an AGN. We examine the optical emission
line ratios of our X-ray selected sample and find that optical AGN diagnostics
fail to identify 85% of the sources. We then calculated the growth rates of the
black holes powering our AGN in terms of their specific accretion rates
($\propto L_\mathrm{X}/M_\mathrm{*}$, an approximate tracer of the Eddington
ratio). Within our observed sample, we found a wide range of specific accretion
rates. After correcting the observed sample for the varying sensitivity of
3XMM, we found further evidence for a wide range of X-ray luminosities and
specific accretion rates, described by a power law. Using this corrected AGN
sample we also define an AGN fraction describing their relative incidence
within the parent sample. We found the AGN fraction increases with host galaxy
mass (up to $\approx$ 6%) for galaxies with X-ray luminosities between $10^{39}
\mathrm{erg/s}$ and $10^{42} \mathrm{erg/s}$, and by extrapolating the power
law to higher luminosities, we found evidence to suggest the fraction of
luminous AGN ($L_\mathrm{X} \geq 10^{42.4} \mathrm{erg/s}$) is constant out to
$z \approx 0.7$.
