A0243
Title: Saddle point approximations for the tests of covariance matrices from decomposable Gaussian graphical models
Authors: Yanyan Wu - University of Hawaii at Manoa (United States) [presenting]
Abstract: The aim is to consider a classical testing problem of equal covariance matrices from Gaussian models with conditional independences and is Markov with respect to a decomposable graph. Under these conditional independences, the dimension of the parameter space is then reduced significantly and can be represented by a directed acyclic graph (DAG). Such models are important for high-dimensional or sparse data in many fields, such as finance, marketing or genomics. Under the null hypothesis, the likelihood ratio test statistics (LRT), derived from the hyper Wishart distribution according to the DAG, follows a chi-square distribution and has the first-order accuracy. The proposed saddle point approximation method had a third-order of accuracy. Briefly, the derivation of the method involved (a) computation of the modified LRT, Bartlett Box M-statistic, which improved the accuracy of the test to the 2nd-order, (b) derivation of the cumulant generating function of the M-statistic, and (c) application of the Lugannani-Rice formula to the cumulative generating function. Simulation studies show that the proposed method has extremely accurate tail coverages even when the sample size is small.
