Seminar Room, Herschel Smith Building, University Forvie Site
Please note the change of time and location. The Hershel Smith Building is across the car park from the Institute of Public Health. For a map, see https://map.cam.ac.uk/Forvie+Site.
Dr Rajen Shah
University of Cambridge
“Goodness of Fit Tests for High-Dimensional Linear Regression”
Abstract:While there are now many procedures available for obtaining the significance of variables or groups of variables in high-dimensional linear models, we do not have a corresponding array of diagnostic tests to check whether the high-dimensional linear model is itself correct. In this talk, I will introduce a family of goodness of fit tests, which we call Residual Prediction (RP) tests, that aim to fill this crucial gap in the practitioner’s toolbox. One of our main contributions is a method for simulating from (essentially) the exact distribution of the scaled residuals following a Lasso fit, under the null hypothesis that the high-dimensional linear model is correct. This allows a whole range of tests to be constructed that are tailored to detect specific departures from the null model, and critical values can be determined easily by Monte Carlo without having to resort to complicated analyses of (aysmptotic) distributions of test statistics. RP tests can be used to test for significance of groups of variables as a special case, but can also be designed to test for as diverse model mis-specifications as heteroscedasticity and different types of non-linearity. This is joint work with Peter Bühlmann (ETH Zurich).
To see the full programme for the MRC Biostatistics Unit Seminar Series this term please visit https://www.mrc-bsu.cam.ac.uk/news-and-events/seminars/