A Method Of Complete Independence Test In High-dimensional Discrete Data

In classical statistical theory, we assume that the dimension of data is fixed, sample size tend to be infinite. However, high-dimensional data analysis theory means that the dimension of data tend to be infinite as the sample size. Particularly, when the dimension of data is more than sample size, we call it ultra high dimensional data. With the development of science and technology, economy, data is increasingly tend to be complex. Compared to the sample size, the dimension of data is no longer a small amount, even greater than the sample size. This brings to the classical statistical method and theory the big challenges. So we need to analyze problems with high dimension.At present, people have presented a lot of methods about independence in high-dimensional data. For example, Schott[1]have presented statistical methods based on pearson correlation coefficient. Zou and Wang[2]have presented statistical methods based on rank correlation coefficient. However, these methods are for the case of high-dimensional continuous data.Therefore, this paper presents a test for complete independence in high-dimensional discrete data. Based on the correlation coefficient, this paper proposes a new statistic. We use this statistic to test complete independence in high-dimensional discrete data. Because the form of the test statistic given in this paper is slightly more complicated, asymptotic distribution of the statistic are not readily available. We use permutation test. Finally, through the simulation study, we get the error type and power. In the process of simulation, we get the change trend of error type and power. Through the simulation study, we compare our method with pearson method. Results show that our method is more effective for high dimensional discrete data.