  We calculate an empirical, non-parametric estimate of the shape of the
period-marginalized radius distribution of planets with periods less than 150
days using the small yet well-characterized sample of cool ($T_{\rm eff} <4000
$K) dwarf stars in the Kepler catalog. In particular, we present and validate a
new procedure, based on weighted kernel density estimation, to reconstruct the
shape of the planet radius function down to radii smaller than the completeness
limit of the survey at the longest periods. Under the assumption that the
period distribution of planets does not change dramatically with planet radius,
we show that the occurrence of planets around these stars continues to increase
to below 1 $R_\oplus$, and that there is no strong evidence for a turnover in
the planet radius function. In fact, we demonstrate using many iterations of
simulated data that a spurious turnover may be inferred from data even when the
true distribution continues to rise toward smaller radii. Finally, the sharp
rise in the radius distribution below $\sim$3 $R_\oplus$ implies that a large
number of planets await discovery around cool dwarfs as the sensitivities of
ground-based transit surveys increase.
