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A nonparametric two‐sample test using a general φ ‐divergence‐based mutual information
Author(s) -
Guha Apratim,
Biswas Atanu,
Ghosh Abhik
Publication year - 2021
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/stan.12232
Subject(s) - nonparametric statistics , mathematics , divergence (linguistics) , sample (material) , kullback–leibler divergence , independence (probability theory) , random variable , statistics , philosophy , linguistics , chemistry , chromatography
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 ( φ DMI) 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 φ DMI. 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.