Estimation Of Covariance Matrix With Spherical Condition And Its Application

Covariance estimation is a regular statical problem widely found in research fields such as risk management,machine learning etc.Recently,more scholars switched their focus to conditional covariance problems to resolve practical issues.Recent studies provide a model of nonparametric estimation of the covariance matrix for single dimensional condition variables.However,the studies on the estimation of covariance matrix for two or more-dimensional condition variables are few.On the surface of the circle and sphere,the coordinates of the data points are discontinuous,which makes the traditional Gaussian kernel as the kernel function of the nonparametric estimation model no longer applicable.This article provides a model of nonparametric covariance matrix estimation with spherical condition variables.A spherical kernel is introduced for estimation of covariance matrix which provides corresponding asymptotic properties,the application of the model in simulation experiment and actual data.The simulation experiment shows that the Spherical kernel has a more accurate estimation than the Gaussian kernel in covariance matrix with spherical condition variables.In the actual data experiment,the model is applied to estimate the covariance matrix of wind speed,rainfall and temperature with wind direction as conditional variable.The result shows that when the wind direction is about 0 degrees,the Gaussian kernel estimates the wrong correlation,while the spherical kernel gives a result that is consistent with the actual situation.Therefore,the Spherical kernel is more accurate in reflecting the relationship between variables.