부산대학교 도서관

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 Ywith Rcategories and a continuous random variable X. They ingeniously proved the asymptotic normality of the MV test statistic when Rdiverges to infinity, which brings many merits to the MV test, including making it more convenient for independence testing when Ris 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 Ris 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.