Title: Measuring conditional dependence using the local Gaussian partial correlation
Authors: Haakon Otneim - Norwegian School of Economics (Norway) [presenting]
Dag Tjoestheim - University of Bergen (Norway)
Abstract: It is well known 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 and conditional correlations. The partial correlation does not, however, characterize conditional dependence in many non-Gaussian populations. We introduce 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 on this, both simulated and real, and derive estimation theory under a local likelihood framework. Finally, we indicate how the LGPC can be used to construct a powerful test for conditional independence, which, again, can be used to detect Granger causality in time series.