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A distribution-free test of independence based on a modified mean variance index

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Listed:
  • Weidong Ma
  • Fei Ye
  • Jingsong Xiao
  • Ying Yang

Abstract

Cui and Zhong (2019), (Computational Statistics & Data Analysis, 139, 117–133) proposed a test based on the mean variance (MV) index to test independence between a categorical random variable Y with R categories and a continuous random variable X. They ingeniously proved the asymptotic normality of the MV test statistic when R diverges to infinity, which brings many merits to the MV test, including making it more convenient for independence testing when R is large. This paper considers a new test called the integral Pearson chi-square (IPC) test, whose test statistic can be viewed as a modified MV test statistic. A central limit theorem of the martingale difference is used to show that the asymptotic null distribution of the standardized IPC test statistic when R is diverging is also a normal distribution, rendering the IPC test sharing many merits with the MV test. As an application of such a theoretical finding, the IPC test is extended to test independence between continuous random variables. The finite sample performance of the proposed test is assessed by Monte Carlo simulations, and a real data example is presented for illustration.

Suggested Citation

  • Weidong Ma & Fei Ye & Jingsong Xiao & Ying Yang, 2023. "A distribution-free test of independence based on a modified mean variance index," Statistical Theory and Related Fields, Taylor & Francis Journals, vol. 7(3), pages 235-259, July.
    • Handle: RePEc:taf:tstfxx:v:7:y:2023:i:3:p:235-259
    DOI: 10.1080/24754269.2023.2201101
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