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A nonparametric two‐sample test using a general φ‐divergence‐based mutual information

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  • Apratim Guha
  • Atanu Biswas
  • Abhik Ghosh

Abstract

Nonparametric two‐sample problems are extremely important for applications in different applied disciplines. We define a general MI based on the φ divergences and use its estimate to propose a new general class of nonparametric two sample tests for continuous distributions. We derive the asymptotic distribution of the estimates of φ‐divergence‐based MI (φDMI) under the assumption of independence in the hybrid setup of one binary and one continuous random variables. Additionally, for finite sample cases, we describe an algorithm for obtaining the bootstrap‐based critical value of our proposed two‐sample test based on the estimated φDMI. We demonstrate through extensive simulations that the proposed class of tests work exceptionally well in many situations and can detect differences where other two‐sample tests fail. Finally, we analyze an application of our proposed tests to assess a solution to information leakage in e‐passport data.

Suggested Citation

  • Apratim Guha & Atanu Biswas & Abhik Ghosh, 2021. "A nonparametric two‐sample test using a general φ‐divergence‐based mutual information," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(2), pages 180-202, May.
    • Handle: RePEc:bla:stanee:v:75:y:2021:i:2:p:180-202
    DOI: 10.1111/stan.12232
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    References listed on IDEAS

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    1. Liu, Yukun & Zou, Changliang & Zhang, Runchu, 2008. "Empirical likelihood for the two-sample mean problem," Statistics & Probability Letters, Elsevier, vol. 78(5), pages 548-556, April.
    2. Micheas, Athanasios C. & Zografos, Konstantinos, 2006. "Measuring stochastic dependence using [phi]-divergence," Journal of Multivariate Analysis, Elsevier, vol. 97(3), pages 765-784, March.
    3. Atanu Biswas & Maria Carmen Pardo & Apratim Guha, 2014. "Auto-association measures for stationary time series of categorical data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 487-514, September.
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