Title: A Bartlett-type correction for likelihood ratio tests with application to testing equality of Gaussian graphical models Authors:  Vera Djordjilovic - Ca' Foscari University of Venice (Italy) [presenting]
Abstract: The classical problem of testing the equality of two p-variate normal distributions is studied. The likelihood ratio test (LRT) offers an elegant solution to this problem. LRT statistic has an asymptotic chi-square distribution, which can be inaccurate for low sample sizes (n) or when the dimension of the distributions, p, is close to the sample size, n. A multiplicative correction for the LRT statistic is proposed which improves its performance in terms of accuracy and the phase transition boundary is proved for the new test statistic is 1, meaning that the chi-square approximation will hold whenever p/n tends to zero. The usefulness of our proposal in the context of Gaussian graphical models is shown.