IMS
Session Slot: 8:30-10:20 Wednesday
Estimated Audience Size:
AudioVisual Request: Two Overheads
Session Title: Inference from Small Samples
Theme Session: No
Applied Session: No
Session Organizer: Davison, A. C. Swiss Federal Institute of Technology, Lausanne
Address: Department of Mathematics
Swiss Federal Institute of Technology
1015 Lausanne
Switzerland
Phone: (41)-(0)21-693-5502
Fax: (41)-(0)21-693-4250
Email: davison@dma.epfl.ch
Session Timing: 110 minutes total (Sorry about format):
Opening Remarks by Chair - 5 minutes First Speaker - 25 minutes Second Speaker - 25 minutes Third Speaker - 25 minutes Discussant - 10 minutes Floor Discussion - 10 minutes
Session Chair: Wang, Soujin Texas A&M University
Address: Department of Statistics
Texas A&M University
College Station, TX 77843
Phone: 409-845-3164
Fax: 409-845-3144
Email: sjwang@stat.tamu.edu
1. Adjustments to the Likelihood Ratio Statistic
Severini, Thomas A., Northwestern University
Address: Department of Statistics
Northwestern
University
2006 Sheridan Road
Evanston IL 60208
USA
Phone: (1)-847-467-1254
Fax: (1)-847-491-4939
Email: severini@nwu.edu
Abstract: Consider a model parameterized by a scalar parameter of interest as well as a nuisance parameter. Inference about the parameter of interest may be based on R, the signed square root of the likelihood ratio statistic. The distribution of R may be approximated, to first order, by a standard normal distribution. To improve the accuracy of this normal approximation, several modifications to R have been proposed. In this talk, I will discuss the properties of Barndorff-Nielsen's modified directed likelihood statistic, R*, along with approximations to R* that are more convenient to use in practice. In particular, I will present an approximation to R* that can be calculated numerically for a wide range of models. The results will be illustrated on several examples.
2. Technology Transfer: Implementing Small-Sample Methods
Davison, Anthony C., Swiss Federal Institute of Technology, Lausanne
Address: Department of Mathematics
Swiss Federal Institute of Technology
1015 Lausanne
Switzerland
Phone: (41)-(0)21-693-5596
Fax: (41)-(0)21-693-4250
Email: Anthony.Davison@epfl.ch
Abstract: Over the past two decades there has been rapid theoretical progress on small-sample asymptotics for parametric statistical models, and although the theory remains incomplete many aspects are now well-understood. However, compared to competing technology such as the bootstrap and Markov chain Monte Carlo methods, small-sample parametric theory seems to have been under-used in applications. One reason for this may be the sometimes forbidding mathematics used, but probably more important is the lack of software with which to apply the parametric approximations in routine data analysis.
In this talk I shall briefly outline what seems to me to be the state of the art in implementation of nonparametric small-sample inference, with special reference to a S-Plus library of bootstrap functions written by A. J. Canty. Then I shall describe the initial phase of work on implementing small-sample parametric methods, which is being performed by A. R. Brazzale, with the goal of making use of r* and related approximations as straightforward as the use of nonparametric methods, in order that wider numerical experience of parametric methods can be gained by the developers and consumers of small-sample asymptotics.
3. Exact Inference for Sparse Contingency Tables Using Markov Chain Monte Carlo Methods
Smith, Peter W. F., University of Southampton
Address: Department of Social Statistics
University of Southampton
Highfield
Southampton SO17 1BJ
UK
Phone: (44)-(0)1703-593191
Fax: (44)-(0)1703-593846
Email: pws@soton.ac.uk
Abstract: When analysing sparse contingency tables inferences based on asymptotic distributions may be unreliable, especially for goodness-of-fit tests, and inferences based on exact distributions are preferred. I will present, for a log-linear model, the form of the exact conditional distribution of a sufficient statistic for the interest parameters, given the sufficient statistic for the nuisance parameters. In general, direct generation from this distribution is infeasible. I will describe Markov chain Monte Carlo methods for generating from the conditional distribution. These methods enable estimation of the exact conditional p-value and the exact distribution of the residuals for log-linear models. Examples will include tests of goodness of fit of the all-two-way interaction model, the quasi-symmetry model and the uniform association model. Tests against non-saturated alternatives will also be considered. I will conclude by briefly discussing irreducibility of the Markov chains and other methods for generating from the exact conditional distribution.
Discussant: Davison, A. C. Swiss Federal Institute of Technology, Lausanne
Address: Department of Mathematics
Swiss Federal Institute of Technology
1015 Lausanne
Switzerland
Phone: (41)-(0)21-693-5502
Fax: (41)-(0)21-693-4250
Email: davison@dma.epfl.ch
List of speakers who are nonmembers: A. R. Brazzale, P. W. F. Smith