Local Linear Estimation For Generalized Measures Of Correlation

The correlation coefcient between variables has attracted much attention in thestatistical research, it plays an important role in the model selection, dimensional-ity reduction of high-dimensional data. Pearson correlation coefcient has been themost widely used measurement method, but it has some limitations. Such as it canonly measure the symmetry relation of linear. To overcome these limitations, newmeasuring methods of correlation have been proposed by many scholars. Zheng et al.(2012)[1]proposed an index which can measure nonlinear or asymmetry correlation.Zheng et al.(2012) used Kernel estimation method to estimate GMC. This papergives a new estimation of GMC with Local linear regression method, and compare itwith Kernel method. Simulation results will show the advantages and disadvantagesof two methods in the estimation of GMC.