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The problem of parameter estimation and of the evaluation of related uncertainty intervals is considered in the case that a probabilistic description of noise and errors is not available (of suitable), but only a bound on them is known. In the present paper only linear parametrizations and estimators are considered. Very simple and computationally feasible algorithms are derived for evaluating two different types of uncertainty intervals (Estimates Uncertainty Intervals, Parameter Uncertainty Intervals). The relationships between the EUI's and the PUI's are established, and the solution to the problem of the minimum uncertainty intervals estimator is given: the latter can be obtained by means of a simple linear programming algorithm.