| With the arrival of the era of data explosion,the requirements for the ability to obtain information in data are increasingly high,and the analysis of data often needs to explore the correlation between variables.Correlation test is an important means to study the correlation between variables,which is widely used in many fields such as economy,environmental science,biology and medicine.With the increasing amount of data,the correlation between data is no longer limited to simple linear relationship,but also exists many complex correlation relationships.Distance correlation coefficient is a common nonlinear relationship test method.Heller et al.aggregated some test statistics and proposed a distance-based non-parametric test method,called HHG algorithm.However,HHG algorithm uses the chi-square test method,and the square in the chi-square test will cause some numbers to become smaller after the square,and the obtained test statistics will become smaller,thus leading to inaccurate results.Based on this,we propose to improve the HHG algorithm by changing the square in the chi-square test to the absolute value,so as to improve the test effect.Another way to implement the HHG algorithm is to first partition the sample,divide the observation point into several cells,and then calculate the Pearson score for each cell.Also,because the square in the Pearson score will cause some numbers to become smaller after being squared,the obtained test statistics will become smaller,resulting in inaccurate results,we change the square in the Pearson score to the absolute value.The statistics for all partitions are then summed to get the test statistics.We also considers the case where some prior information is known,that is,when the correlation between known variables exists only among some components,the prior information can be used to eliminate the components with no correlation at all,redefine ”distance” in HHG algorithm,and take the distance between components with correlation as ”distance” in HHG.The correlation test method proposed in this paper shows good robustness in simulation experiments,and shows good test effect for different types of correlation relationships between variables given,also better than the orginal algorithm in most cases.Finally,in the real data experiment,the improved algorithm detects more number of correlations between the target variables in most cases than other methods,which indicates that the improved algorithm has improved the inspection effect. |
