Type: Seminar

Distribution: World

Expiry: 13 Sep 2013

CalTitle1: AGR Seminar: Confidence sets for variable selection

Auth: mathas@gdh-47.on.site.uni-stuttgart.net in SMS-auth

**Host venue**

La Trobe University

**Abstract**

We introduce the notion of variable selection confidence set (VSCS) for linear regression based on F-testing. The VSCS extends the usual notion of confidence intervals to the variable selection problem: A VSCS is a set of regression models that contains the true model with a given level of confidence. For noisy data, distinguishing among competing models is usually very difficult and the VSCS will contain many models; if the data are really informative, the VSCS will contain a much smaller number of useful models. We advocate special attention to the set of lower boundary models (LBMs), which are the most parsimonious models that are not statistically significantly inferior to the full model at a given confidence level. Based on the LBMs, variable importance and measures of co-appearance importance of predictors can be naturally defined. Up to date, an almost exclusive emphasis has been on selecting a single model or two. In the presence of a number of predictors, especially when the number of predictors is comparable to (or even larger than) the sample size, the hope of identifying the true or the unique best model is often unrealistic. Consequently, a better approach is to select a relatively small set of models that all can more or less adequately explain the data at the given confidence level. This strategy identifies the most important variables in a principled way that goes beyond simply trusting the single lucky winner based on a model selection criterion.

**Seminar convenor**

Dr Andriy Olenko

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If you would like to attend this seminar in our access grid room then please check to see if the grid is already booked at this time and send an email to accessgridroom@maths.usyd.edu.au to let the CSOs know that you would like to attend.