Estimation of a distribution function by extrapolating upper and lower bounds

Constrained optimization is proposed as a practical solution to the problem of estimating a distribution function at each point in a given set from monotone sequences of upper and lower bounds. The proposed solution employs least absolute value estimation and, hence, has a linear programming formulation. The special structure inherent in this formulation is exploited and an efficient computational method is discussed. The procedure is illustrated by two examples.