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Expected Conditional Characteristic Function-based Measures for Testing Independence

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  • Chenlu Ke
  • Xiangrong Yin

Abstract

We propose a novel class of independence measures for testing independence between two random vectors based on the discrepancy between the conditional and the marginal characteristic functions. The relation between our index and other similar measures is studied, which indicates that they all belong to a large framework of reproducing kernel Hilbert space. If one of the variables is categorical, our asymmetric index extends the typical ANOVA to a kernel ANOVA that can test a more general hypothesis of equal distributions among groups. In addition, our index is also applicable when both variables are continuous. We develop two empirical estimates and obtain their respective asymptotic distributions. We illustrate the advantages of our approach by numerical studies across a variety of settings including a real data example. Supplementary materials for this article are available online.

Suggested Citation

  • Chenlu Ke & Xiangrong Yin, 2020. "Expected Conditional Characteristic Function-based Measures for Testing Independence," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(530), pages 985-996, April.
    • Handle: RePEc:taf:jnlasa:v:115:y:2020:i:530:p:985-996
    DOI: 10.1080/01621459.2019.1604364
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    Cited by:

    1. Lu, Jun & Lin, Lu & Wang, WenWu, 2021. "Partition-based feature screening for categorical data via RKHS embeddings," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    2. Zhang, Wei & Gao, Wei & Ng, Hon Keung Tony, 2023. "Multivariate tests of independence based on a new class of measures of independence in Reproducing Kernel Hilbert Space," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    3. Ke, Chenlu & Yang, Wei & Yuan, Qingcong & Li, Lu, 2023. "Partial sufficient variable screening with categorical controls," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    4. Meintanis, Simos G. & Hušková, Marie & Hlávka, Zdeněk, 2022. "Fourier-type tests of mutual independence between functional time series," Journal of Multivariate Analysis, Elsevier, vol. 189(C).

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