We are pleased to announce that our paper
Confidence intervals with imprecise data
has been accepted for publication in Statistical Papers.
This paper, written by Darío Tagarro, Raúl Pérez-Fernández and Enrique Miranda, addresses the problem of accounting for imprecision in the process of measuring a continuous variable in the context of confidence intervals for parameters of probability distributions. We generalize the classical notion of confidence interval in the presence of imprecision by introducing the notions of inner and outer confidence interval, studying different properties of both mathematical constructs and providing their explicit expressions in five prominent cases in the field of Statistics.
After introducing in Section 2 some basic concepts on random sets, random intervals and confidence intervals, we give our definition of the inner and outer confidence intervals in Section 3. In Section 4 we present some properties related to their coverage and characterization. In particular, we derive an explicit expression of both constructs in terms of the extrema of the lower and upper bound functions of the confidence interval. Finally, we discuss in Section 5 five relevant examples of confidence intervals and provide the explicit formulae of the inner and outer confidence intervals under imprecision. For this aim, we have introduced the notions of quasivertex and 2-quasivertex, that have allowed us to simplify the optimization problem associated with the computation of the inner and outer intervals.