Approach to Analysis of Self-Selected Interval Data

We analyze an approach to quantitative information elicitation in surveys that includes many currently popular variants as special cases. Rather than asking the individual to state a point estimate or select between given brackets, the individual can self-select any interval of choice. We propose a new estimator for such interval censored data. It can be viewed as an extension of Turnbull's estimator (Turnbull(1976)) for interval censored data. A detailed empirical example is provided, using a survey on the valuation of a public good. We estimate survival functions based on a Weibull and a mixed Weibull/exponential distribution and prove that a consistent maximum likelihood estimator exists and that its accuracy can be consistently estimated by re-sampling methods in these two families of distributions.