  The paper presents a novel asymptotic distribution for a mle when the
log--likelihood is strictly concave in the parameter for all data points; for
example, the exponential family. The new asymptotic distribution can be seen as
a refinement of the usual normal asymptotic distribution and is comparable to
an Edgeworth expansion. However, it is obtained with weaker conditions than
even those for asymptotic normality. The same technique is then used to find
the exact distribution of the weighted likelihood bootstrap sampler.
