Stochastic frontier estimation is proposed as a method to fit either maximum or minimum relationships. This procedure represents an improvement over the practice of using ordinary least squares estimation to fit average relationships of extreme data in subclasses. Using ordinary least squares to estimate maximum or minimum relationships requires data reduction that causes two problems, a loss of information and the introduction of sample selection bias. Because stochastic frontier estimation does not require data reduction, the two problems with least squares estimation are avoided. The stochastic frontier estimation technique is demonstrated by fitting a nonlinear function to the shape of the loblolly pine ( Pinus taeda ) tree crown. The crown shape model relates the maximum observed crown radius to the relative crown length. Maximum-likelihood via the expectation-maximization algorithm is used to estimate the parameters of the model.