|
Activity Number:
|
113
|
|
Type:
|
Contributed
|
|
Date/Time:
|
Monday, August 3, 2009 : 8:30 AM to 10:20 AM
|
|
Sponsor:
|
Section on Statistical Computing
|
| Abstract - #304974 |
|
Title:
|
On the Behrens-Fisher Problem: A Globally Convergent Algorithm and a Finite-Sample Study of the Wald, LR, and LM Tests
|
|
Author(s):
|
Alexandre Belloni*+ and Gustavo Didier
|
|
Companies:
|
Duke University and Tulane University
|
|
Address:
|
Fuqua School of Business, Durham, NC, 27708-0120,
|
|
Keywords:
|
Behrens-Fisher Problem ; hypothesis testing ; Likelihood Ratio Test ; algorithm ; high-dimensional data
|
|
Abstract:
|
In this paper we provide a provably convergent algorithm for the multivariate Gaussian Maximum Likelihood version of the Behrens-Fisher problem. Our work builds upon a formulation of the log-likelihood function proposed by Buot and Richards. Instead of focusing on the first order optimality conditions, the algorithm aims directly for the maximization of the log-likelihood function itself to achieve a global solution. Convergence proof and complexity estimates are provided for the algorithm. Computational experiments illustrate the applicability of such methods to high-dimensional data. We also discuss how to extend the proposed methodology to a broader class of problems. We establish a systematic algebraic relation between the Wald, Likelihood Ratio and Lagrangian Multiplier Test (W >= LR >= LM) in the context of the Behrens-Fisher problem.
|
