SOME RECENT RESULTS IN MODEL SELECTION - Quantitative Medical Data Analysis Using Mathematical Tools and Statistical Techniques - page 25

CHAPTER 2

SOME RECENT RESULTS IN MODEL SELECTION

Xiaoming Huo a;b and Xuelei (Sherry) Ni b;c
a Department of Statistics, University of California at Riverside,
Riverside, CA, USA
b School of Industrial and Systems Engineering,
Georgia Institute of Technology,
765 Ferst Dr. Atlanta, GA 30332-0205, USA
E-mails: a [e-mail]
c [e-mail]

In statistics, model selection has a long standing history, while new re-
sults in this area still keep coming. At this point, it is nearly impossible
and not helpful to give a comprehensive survey on all the available the-
orems. We take a special angle: from where more results are likely to be
generated. Our perspective is based on some recent interesting ndings
in applied mathematics; namely, in some cases a subset of NP hard prob-
lems can be solved eectively by some convex optimization approaches,
which only require polynomial time. We discuss the potential of this ap-
proach. For users who would like to know more about the existing ideas
in model selection, we provide a summary in the end.

1. Introduction

Model selection is a classical topic in statistics. Here, for simplicity, we
restrict to an ordinary linear regression model. For classical results, an
excellent survey is given by George 22 , while Kadane and Lazar 29 give a
superior survey from a Bayesian viewpoint. Since their appearance, many
new interesting results have come out. Presenting all of them here is nearly
impossible and also distractive. As anticipated, researchers have taken dif-
ferent angles in tackling the model selection problem.
The perspective taken in this paper is new. It can be summarized into
the following three steps.

First of all, it is proven (see [28]) that many classical criteria