Working paper: Two-step approach to Self-Selected Interval Data in Elicitation Surveys by Yuri Belyaev and Bengt Kriström.
In this paper the authors propose a novel two-step approach to elicitation in surveys that combine self-selected intervals in a first step, and then employ brackets generated from the intervals in a second step, thus combining the advantages of self-selected intervals with the usefulness of brackets. By generating the brackets from the first sample the problem of the optimal design of brackets and additional assumptions on dependency between the self-selected intervals and their points of interest are avoided.
The set-up necessitates development of new statistical models. First, the authors propose a stopping rule for sampling in the first step. Second, Theorem 1 proves that the proposed non-parametric ML-estimator of the underlying distribution function is consistent. Third, a special recursion for quick estimation of the ML- estimators is suggested. Theorem 2 shows that the accuracy of the estimator can be consistently estimated by resampling.
Read the Working Paper