  Interferometric radius measurements provide a direct probe of the fundamental
parameters of M dwarfs, but is within reach for only a limited sample of
nearby, bright stars. We use interferometrically-measured radii, bolometric
luminosities, and effective temperatures to develop new empirical calibrations
based on low-resolution, near-infrared spectra. We use H-band Mg and Al
features to derive calibrations for effective temperature, radius and log
luminosity; the standard deviations in the residuals of our best fits are,
respectively, 73K, 0.027Rsun, and 0.049 dex (11% error on luminosity). These
relationships are valid for mid K to mid M dwarf stars, roughly corresponding
to temperatures between 3100 and 4800K. We apply our calibrations to M dwarfs
targeted by the MEarth transiting planet survey and to the cool Kepler Objects
of Interest (KOIs). We independently validate our calibrations by demonstrating
a clear relationship between our inferred parameters and the absolute K
magnitudes of the MEarth stars, and we identify objects with magnitudes too
bright for their estimated luminosities as candidate multiple systems. We also
use our inferred luminosities to address the applicability of near-infrared
metallicity calibrations to mid and late M dwarfs. The temperatures we infer
for the KOIs agree remarkably well with those from the literature; however, our
stellar radii are systematically larger than those presented in previous works
that derive radii from model isochrones. This results in a mean planet radius
that is 15% larger than one would infer using the stellar properties from
recent catalogs. Our results confirm those of previous in-depth studies of
Kepler-42, Kepler-45, and Kepler-186.
