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Consider a linear regression model where some or all of the observations of the dependent variable have been either rounded or interval-censored and only the resulting interval is available. Given a linear estimator β of the vector of regression parameters, we consider its possibilistic generalization for the model with rounded/censored data, which is called the OLS-set in the special case β = Ordinary Least Squares. We derive a geometric characterization of the set: we show that it is a zonotope in the parameter space. We show that even for models with a small number of regression parameters and a small number of observations, the combinatorial complexity of the polyhedron can be high. We therefore derive simple bounds on the OLS-set. These bounds allow to quantify the worst-case impact of rounding/censoring on the estimator β . This approach is illustrated by an example. We also observe that the method can be used for quantification of the rounding/censoring effect in advance, before the experiment is made, and hence can provide information on the choice of measurement precision when the experiment is being planned.

The paper deals with the inverse linear programming problem over intervals. More precisely, given interval domains for the objective function coefficients and constraint coefficients of a linear program, we ask for which scenario a prescribed optimal value is attained. Using continuity of the optimal value function (under some assumptions), we propose a method based on parametric linear programming techniques. We study special cases when the interval coefficients are situated in the objective function and/or in the right-hand sides of the constraints as well as the generic case when possibly all coefficients are intervals. We also compare our method with the straightforward binary search technique. Finally, we illustrate the theory by an accompanying numerical study, called "Matrix Casino", showing some approaches to designing a matrix game with a prescribed game value.