Uniformly most powerful unbiased test for conditional independence in Gaussian graphical model

TL;DR

This paper proves that the partial correlation test is the uniformly most powerful unbiased test for pairwise conditional independence in Gaussian graphical models, confirming its optimality in model selection.

Contribution

The paper establishes that the partial correlation test is the uniformly most powerful unbiased test for conditional independence in Gaussian models, resolving a longstanding question.

Findings

Partial correlation test is uniformly most powerful unbiased.

The test can be reduced to the Neymann structure.

Implications for Gaussian graphical model selection.

Abstract

Model selection for Gaussian concentration graph is based on multiple testing of pairwise conditional independence. In practical applications partial correlation tests are widely used. However it is not known whether partial correlation test is uniformly most powerful for pairwise conditional independence testing. This question is answered in the paper. Uniformly most powerful unbiased test of Neymann structure is obtained. It turns out, that this test can be reduced to usual partial correlation test. It implies that partial correlation test is uniformly most powerful unbiased one.