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Imprecise Imputation: A Nonparametric Micro Approach Reflecting the Natural Uncertainty of Statistical Matching with Categorical Data

Author

Listed:
  • Endres Eva

    (Ludwig-Maximilians-University of Munich, Ludwigstrasse 33, 80539Munich, Germany.)

  • Fink Paul

    (Ludwig-Maximilians-University of Munich, Ludwigstrasse 33, 80539Munich, Germany.)

  • Augustin Thomas

    (Ludwig-Maximilians-University of Munich, Ludwigstrasse 33, 80539Munich, Germany.)

Abstract
Statistical matching is the term for the integration of two or more data files that share a partially overlapping set of variables. Its aim is to obtain joint information on variables collected in different surveys based on different observation units. This naturally leads to an identification problem, since there is no observation that contains information on all variables of interest.We develop the first statistical matching micro approach reflecting the natural uncertainty of statistical matching arising from the identification problem in the context of categorical data. A complete synthetic file is obtained by imprecise imputation, replacing missing entries by sets of suitable values. Altogether, we discuss three imprecise imputation strategies and propose ideas for potential refinements.Additionally, we show how the results of imprecise imputation can be embedded into the theory of finite random sets, providing tight lower and upper bounds for probability statements. The results based on a newly developed simulation design–which is customised to the specific requirements for assessing the quality of a statistical matching procedure for categorical data–corroborate that the narrowness of these bounds is practically relevant and that these bounds almost always cover the true parameters.

Suggested Citation

  • Endres Eva & Fink Paul & Augustin Thomas, 2019. "Imprecise Imputation: A Nonparametric Micro Approach Reflecting the Natural Uncertainty of Statistical Matching with Categorical Data," Journal of Official Statistics, Sciendo, vol. 35(3), pages 599-624, September.
    • Handle: RePEc:vrs:offsta:v:35:y:2019:i:3:p:599-624:n:5
    DOI: 10.2478/jos-2019-0025
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    References listed on IDEAS

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    1. Conti, Pier Luigi & Marella, Daniela & Scanu, Mauro, 2008. "Evaluation of matching noise for imputation techniques based on nonparametric local linear regression estimators," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 354-365, December.
    2. Rebecca R. Andridge & Roderick J. A. Little, 2010. "A Review of Hot Deck Imputation for Survey Non‐response," International Statistical Review, International Statistical Institute, vol. 78(1), pages 40-64, April.
    3. Pier Luigi Conti & Daniela Marella & Mauro Scanu, 2017. "How far from identifiability? A systematic overview of the statistical matching problem in a non parametric framework," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(2), pages 967-994, January.
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