Graduate Student Seminar

Speaker 1: John Zylstra

Title

Agreement of Solutions to the Multivariate Behrens-Fisher Problem

Abstract

The Behrens-Fisher problem is the test of equality of means of 2 normal populations when variances are unknown and assumed to be unequal.  In the case that the populations are univariate, Welch's canonical solution gives an approximate solution by letting the degrees of freedom of an appropriate t-statistic be equal to a function of the sample variances.  In the multivariate setting, the existence of an optimal test has been proven, but the proof was non-constructive and the conditions for existence guaranteed the solution to have pathological properties.  Thus, approximate solutions in the case that the populations are multivariate have been constructed similar to Welch's univariate solution, whereby the degrees of freedom of an appropriate F-statistic are approximated by functions of the covariance matrices.  We seek to provide a literature review of these results and solutions and to show simulation studies that demonstrate the accuracy of the approximations.

Speaker 2: Qing Ji

Title

Uses of Tree Models in Subgroup Identification

Abstract

The subgroup identification is to determine the heterogeneity in the treatment effect across different subpopulation.  Traditionally, interaction structure in regression model is used to detect subgroups but this approach rely on subjective opinions and requires prior knowledge about subgroups.   If the selections were wrong, it could produce dubious results.  The tree structure is a recursive partitioning method that by design singles out subpopulation based on certain partitioning criteria.  The tree model has been developed intensively in various ways since CART was proposed by Breiman in 1984.  I will introduce some current methods designed for subgroup identification including Interaction Tree (IT), Virtual Twin (VT) and Generalized, Unbiased, Interaction Detection and Estimation (GUIDE).