short talks

Saturday, November 4, 2006 - 9:30am - 10:10am
  • EL algorithm for linear models with missing data
    Nancy Glenn (University of South Carolina)
    Linear regression is one of the most widely used statistical techniques. However, there is
    often a problem of missing response variables in practical applications. The expectation maximization (EM) algorithm is a general iterative algorithm for the analysis of missing data; but it relies on parametric assumptions that are usually not met. We present a nonparametric algorithm--the empirical likelihood (EL) algorithm for linear models with missing data. The EL algorithm's advantage is that it makes no assumptions regarding the form of the underlying distribution of the data. We construct confidence
    intervals for the mean response in the presence of missing responses. We also discuss the power and efficiency of confidence intervals constructed when using the EL algorithm to replace missing responses.
  • Why should I care about Lie groups?
    Edray Goins (Purdue University)
    Sometimes differential equations have an obvious symmetry which leads
    to a natural guess for its solution. The Norwegian mathematician
    Marius Sophus Lie (1842-1899) spent most of his career attempting
    to generalize ideas of fellow Norwegian Niels Henrik Abel (1802-1829) from discrete groups of symmetries of algebraic objects to
    continuous groups of symmetries of topological objects. In the
    process, Lie created a new branch of mathematics which united
    differential geometry and abstract algebra.

    In this talk, we give a brief introduction to the pulchritude of
    Lie's ideas. From the geometric nature of manifolds to the analytic
    nature of differential equations, we discuss the natural group action
    of the space of vector fields of a manifold on itself. We conclude
    the talk with a discussion of the computation of Lie group of the
    real line.