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Differentially Private Goodness-of-Fit Tests for Continuous Variables

Author

Listed:
  • Kwak, Seung Woo
  • Ahn, Jeongyoun
  • Lee, Jaewoo
  • Park, Cheolwoo
Abstract
Data privacy is a growing concern in modern data analyses as more and more types of information about individuals are collected and shared. Statistical analysis in consideration of privacy is thus becoming an exciting area of research. Differential privacy can provide a means by which one can measure the stochastic risk of violating the privacy of individuals that can result from conducting an analysis, such as a simple query from a database and a hypothesis test. The main interest of the work is a goodness-of-fit test that compares the sampled data to a known distribution. Many differentially private goodness-of-fit tests have been proposed for discrete random variables, but little work has been done for continuous variables. The objective is to review some existing tests that guarantee differential privacy for discrete random variables, and to propose an extension to continuous cases via a discretization process. The proposed test procedures are demonstrated through simulated examples and applied to the Household Financial Welfare Survey of South Korea in 2018.

Suggested Citation

  • Kwak, Seung Woo & Ahn, Jeongyoun & Lee, Jaewoo & Park, Cheolwoo, 2024. "Differentially Private Goodness-of-Fit Tests for Continuous Variables," Econometrics and Statistics, Elsevier, vol. 31(C), pages 81-99.
    • Handle: RePEc:eee:ecosta:v:31:y:2024:i:c:p:81-99
    DOI: 10.1016/j.ecosta.2021.09.007
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    References listed on IDEAS

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    1. Wasserman, Larry & Zhou, Shuheng, 2010. "A Statistical Framework for Differential Privacy," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 375-389.
    2. Campano, Fred & Salvatore, Dominick, 2006. "Income Distribution," OUP Catalogue, Oxford University Press, number 9780195300918.
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