A distribution-free test of independence based on a modified mean variance index. (English) Zbl 07740724
Summary: H. Cui and W. Zhong [Comput. Stat. Data Anal. 139, 117–133 (2019; Zbl 1507.62039)] 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.
MSC:
| 62-XX | Statistics |
Keywords:
test of independence; asymptotic null distribution; mean variance index; \(k\)-sample Anderson Darling test statistic; concentration type inequalityCitations:
Zbl 1507.62039References:
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