  Nonparametric data envelopment analysis (DEA) estimators have been widely
applied in analysis of productive efficiency. Typically they are defined in
terms of convex-hulls of the observed combinations of
$\mathrm{inputs}\times\mathrm{outputs}$ in a sample of enterprises. The shape
of the convex-hull relies on a hypothesis on the shape of the technology,
defined as the boundary of the set of technically attainable points in the
$\mathrm{inputs}\times\mathrm{outputs}$ space. So far, only the statistical
properties of the smallest convex polyhedron enveloping the data points has
been considered which corresponds to a situation where the technology presents
variable returns-to-scale (VRS). This paper analyzes the case where the most
common constant returns-to-scale (CRS) hypothesis is assumed. Here the DEA is
defined as the smallest conical-hull with vertex at the origin enveloping the
cloud of observed points. In this paper we determine the asymptotic properties
of this estimator, showing that the rate of convergence is better than for the
VRS estimator. We derive also its asymptotic sampling distribution with a
practical way to simulate it. This allows to define a bias-corrected estimator
and to build confidence intervals for the frontier. We compare in a simulated
example the bias-corrected estimator with the original conical-hull estimator
and show its superiority in terms of median squared error.
