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Maximum likelihood estimation for survey data with informative interval censoring. (English) Zbl 1427.62116

Summary: Interval-censored data may arise in questionnaire surveys when, instead of being asked to provide an exact value, respondents are free to answer with any interval without having pre-specified ranges. In this context, the assumption of noninformative censoring is violated, and thus, the standard methods for interval-censored data are not appropriate. This paper explores two schemes for data collection and deals with the problem of estimation of the underlying distribution function, assuming that it belongs to a parametric family. The consistency and asymptotic normality of a proposed maximum likelihood estimator are proven. A bootstrap procedure that can be used for constructing confidence intervals is considered, and its asymptotic validity is shown. A simulation study investigates the performance of the suggested methods.

MSC:

62N02 Estimation in survival analysis and censored data
62F10 Point estimation
62F25 Parametric tolerance and confidence regions
62D05 Sampling theory, sample surveys

Software:

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References:

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