A seminar by Professor Nicola Sartori from University of Padova
Title: Directional Tests in Gaussian Graphical Models
Abstract: Directional tests for vector parameter hypotheses are based on dimensional reduction, saddlepoint approximation and scalar numerical integration. After a brief general introduction, directional tests are developed to compare incomplete undirected graphs in the context of covariance selection for Gaussian graphical models. The exactness of the underlying saddlepoint approximation is proved for chordal graphs and leads to exact control of the size of the tests. Although exactness is not guaranteed for non-chordal graphs, the ability of the saddlepoint approximation to control the relative error leads the directional test to overperform its competitors even in these cases. The accuracy of the proposal is verified by simulation experiments under challenging scenarios, where inference via standard asymptotic approximations to the likelihood ratio test and some of its higher-order modifications fails.
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