Two-Step Approach to Self-Selected Interval Data in Elicitation Surveys

Nonparametric estimation for self-selected interval data collected through a two-stage approach

“…Remark 3 If n = 0, the log-likelihood (1) has essentially the same form as the one in Belyaev and Kriström (2012).…”

“…For finding the solution of (5), we suggest the following iterative process, which is similar to the one proposed by Belyaev and Kriström (2012):…”

“…For the second question (Qu2) we have considered three different designs: splitting the interval stated at Qu1 into two sub-intervals, into three sub-intervals, and into all sub-intervals v j that it contains. The latter corresponds to the sampling scheme explored by Belyaev and Kriström (2012). In case of a 2-split design, the point of split is chosen equally likely from all the possible points d j that are within the interval.…”

“…4 shows the results for n = 2000. The design, corresponding to the sampling scheme in Belyaev and Kriström (2012), is denoted as "all-split". The error when using the all-split design is fairly close to the error when q j is estimated using the uncensored observations x 1 , .…”

“…All these methods rely on the assumption of noninformative censoring, which implies that the joint distribution of L and R contains no parameters that are involved in the distribution function of X and therefore does not contribute to the likelihood function (see, e.g., Sun 2006). In the sampling schemes considered by Belyaev and Kriström (2010, 2012, 2015 this is not a reasonable assumption, thus the standard methods are not appropriate. The existing methods for analysis of time-to-event data in the presence of informative interval censoring require modeling the censoring process and estimating nuisance parameters (see Finkelstein et al 2002) or making additional assumptions about the censoring process (see Shardell et al 2007).…”