A Modification And Applications Of The Projection Correlation Estimator

In the era of big data,we can use high-dimensional data to make statistical inferences about various economic phenomena,but how to improve the accuracy of highdimensional data inference is a new challenge in statistics.The projection correlation can describe the dependence between two random vectors.The projection correlation has several excellent properties.It is invariant with respect to orthogonal transformations and its estimation is free of tuning parameters and does not require moment conditions on the random vectors.There are two equivalent estimators of the squared projection covariance,which are actually biased.In the case of high dimensions,the original projection correlation may not reflect the true interdependence between variables due to large deviations.To solve this problem,we modify the squared projection covariance,define the modified unbiased projection correlation estimation,and demonstrate the necessity of this modification.The modified projection correlation estimation makes up for the deficiency of current research and provides a more informative sample correlation.Besides,we use Monte Carlo simulation to show the validity of the modified projection correlation estimation in the independence test.Finally,we design two applications to illustrate how to use the modified projection correlation estimation to study the interdependence between economic variables and the operation mechanism of economic systems.In the application I,we use the modified projection correlation estimation and the modified distance correlation estimation to study the non-linear dependence between the stock market and cryptocurrency market under different rolling windows,and analyze the causes of this phenomenon.By selecting the suitable rolling window,investors can quickly capture the significant dependence interval between the two markets,so as to realize the rational allocation of assets.In the application II,we combine the hypothesis testing problem with the estimation problem,and study the influence of the debt level change of listed companies on their profitability under the premise of ensuring the reliability of the model with the test based on the modified projection correlation estimation.We analyze the operating mechanism of this phenomenon and give specific financial structure optimization suggestions for listed companies with different operating conditions.