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

Author

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  • Angel G. Angelov

    (USBE, Umeå University)

  • Magnus Ekström

    (USBE, Umeå University)

Abstract

Self-selected interval data arise in questionnaire surveys when respondents are free to answer with any interval without having pre-specified ranges. This type of data is a special case of interval-censored data in which the assumption of noninformative censoring is violated, and thus the standard methods for interval-censored data (e.g. Turnbull’s estimator) are not appropriate because they can produce biased results. Based on a certain sampling scheme, this paper suggests a nonparametric maximum likelihood estimator of the underlying distribution function. The consistency of the estimator is proven under general assumptions, and an iterative procedure for finding the estimate is proposed. The performance of the method is investigated in a simulation study.

Suggested Citation

  • Angel G. Angelov & Magnus Ekström, 2017. "Nonparametric estimation for self-selected interval data collected through a two-stage approach," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(4), pages 377-399, May.
    • Handle: RePEc:spr:metrik:v:80:y:2017:i:4:d:10.1007_s00184-017-0610-7
    DOI: 10.1007/s00184-017-0610-7
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    References listed on IDEAS

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    1. Belyaev, Yuri & Kriström, Bengt, 2012. "Two-step approach to Self-Selected Interval Data in Elicitation Surveys," CERE Working Papers 2012:10, CERE - the Center for Environmental and Resource Economics.
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    6. Belyaev, Yuri & Kriström, Bengt, 2010. "Approach to Analysis of Self-Selected Interval Data," CERE Working Papers 2010:2, CERE - the Center for Environmental and Resource Economics.
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    Cited by:

    1. Angel G. Angelov & Magnus Ekström, 2019. "Maximum likelihood estimation for survey data with informative interval censoring," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(2), pages 217-236, June.

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