This paper provides an extension of the data envelopment analysis (DEA) method by introducing a frontier estimation and efficiency evaluation model that allows for the possibility of random factors. This is accomplished via a symmetric two-sided error component, in addition to the one-sided component for deviations due to inefficiency that is permitted in the traditional DEA models. The model is formulated as a goal-programming type linear program, and geometric interpretation of the primal and dual variables is provided. This paper also provides an extension of minimum absolute deviation regression models by replacing the restrictive parametric specification with a flexible nonparametric formulation for estimating monotonic and concave functional correspondences. The general model is shown to include both the traditional. DEA model and a minimum absolute deviation regression model. An illustrative application of the basic model to a production situation is also presented.