McMaster University

Graduate Program in Statistics



STATISTICS SEMINAR



SPEAKER:
Alesandra Brazzale,
Institute for Systems Science and Biomedical Engineering
National Research Council,Padova, Italy
Date :Wednesday October 3, 2001.
Time : 3:30pm
Address General Science Building
Room: 207
TITLE:
Higher-order Asymptotics in Practice
ABSTRACT:
Practical use of modern likelihood asymptotics has long been limited by the lack of flexible and easy to use computational tools. Examples of extensive applications in real-life problems are missing. The main obstacle to the implementation of higher-order inference is the trade-off between the excessive complexity of the algebraic calculations involved in the derivation and the numerical efficiency required for routine application of the methods. Despite several efforts, no satisfactory solution to the problem was found, a nearly unsurmountable obstacle being the lack of a suitable environment for both symbolic and numerical computation.

The S-PLUS library HOA ( http://www.ladseb.pd.cnr.it/~brazzale/lib.html) is a large move in the direction of making higher-order asymptotics widely available. It implements some of the more promising small-sample solutions for three widely-used model classes: logistic and loglinear models, linear nonnormal and nonlinear heteroscedastic regression models. The software is easy to use and self-contained and can be applied in routine data analysis. To surmount the barrier mentioned above we had to branch off from what has been until now the dominant approach to the implementation of higher-order solutions. Instead of relying on the symbolic manipulation capabilities of computer algebra systems, we re-expressed the higher-order approximations as functions of elementary building-blocks which can be handled by the numerical computing environment. The symbolic manipulation capabilities of S-PLUS are used to derive the expressions of the building blocks for a specific model.

The talk starts off with a brief review of the three model classes considered and of some of the most promising higher-order methods. We show how these improve classical first-order inference by using the routines in the S-PLUS library HOA. The second part of the talk concentrates on the description of the main implementation strategy that made it possible to implement higher-order asymptotics. We will illustrate this point for the most challenging model class considered, that is for nonlinear heteroscedastic regression models.

About the Speaker
Alesandra Brazzale did her undergraduate work at the University of Padova in Italy where she completed an honours thesis under the direction of Alessandra Salvan in 1996. Subsequently she went to the Swiss Federal Institute of Technology in Lausanne (EPFL) where she did her doctoral work under the supervision of Anthony Davison. Her thesis was entitled Practical Small-Sample Parametric Inference. As part of her undergraduate work she started working on software to implement asymptotic techniques and she continued this during her doctoral work. In 1998 she was the winner of the ASA Statistical Computing Section Student Paper Competition and in April 2001 she was named the recipient of the John M. Chambers Statistical Software Award. After she graduated, Alesandra returned to Padova where she is now a research fellow at the Institute for Systems Science and Biomedical Engineering which is an instute under the direction of the Italian National Research Council.
References


Department of Mathematics and Statistics
Graduate Program in Statistics

This page is maintained by Angelo Canty,
Last updated on September 20, 2001