The Locally Gaussian Partial Correlation
提出局部高斯偏相关系数（LGPC），用于刻画非高斯分布中的条件依赖关系，可区分正负依赖并检测非线性格兰杰因果关系。
It is well known in econometrics and other fields that the dependence structure for jointly Gaussian variables can be fully captured using correlations, and that the conditional dependence structure in the same way can be described using partial correlations. The partial correlation does not, however, characterize conditional dependence in many non-Gaussian populations. This article introduces the local Gaussian partial correlation (LGPC), a new measure of conditional dependence. It is a local version of the partial correlation coefficient that characterizes conditional dependence in a large class of populations. It has some useful and novel properties besides: The LGPC reduces to the ordinary partial correlation for jointly normal variables, and it distinguishes between positive and negative conditional dependence. Furthermore, the LGPC can be used to study departures from conditional independence in specific parts of the distribution. We provide several examples of this, both simulated and real, and derive estimation theory under a local likelihood estimation framework. Finally, we indicate how the LGPC can be used to construct a powerful test for conditional independence, which, for example, can be used to detect nonlinear Granger causality in time series.