The purpose of this paper is to provide a brief and selective survey o
f statistical inference in nonparametric, deterministic, linear progra
mming-based frontier models. The survey starts with nonparametric regu
larity tests, sensitivity analysis, two-stage analysis with regression
, and nonparametric statistical tests. It then turns to the more recen
t literature which shows that DEA-type estimators are maximum likeliho
od, and, more importantly the results concerning the asymptotic proper
ties of these estimators. Also included is a discussion of recent atte
mpts to employ resampling methods to derive empirical distributions fo
r hypothesis testing.