Group for Research in Decision Analysis

# Boundaries, Poisson processes, and linear programs

## Keith Knight

Estimation of boundaries arises naturally in a number of problems, including classification and frontier analysis in economics. Boundary estimators are often the solutions of constrained optimization problems (for example, linear programming problems), and the limit theory for such estimators typically involves point process asymptotics. Moreover, standard asymptotic theory is not typically applicable and alternative approaches (such as epi-convergence) are often useful. Applications to regression quantile estimation (both extreme and central) and maximum margin classification are given.