Prof. Malgorzata Bogdan, University of Wroclaw, Poland (15:00-16:00)

Abstract: Sorted L-One Penalized Estimator is a relatively new convex optimization procedure for identifying predictors in large data bases.
In this lecture we will present the method, some theoretical and empirical results illustrating its properties and the applications in the context of genomic and medical data. Apart from the classical version of SLOPE we will also discuss its spike and slab version, aimed at reducing the bias of estimators of regression coefficients. When discussing SLOPE we will also present some new theoretical results on the probability of discovering the true model by LASSO (which is a specific instance of
SLOPE) and its thresholded version.

Dr. Pauline O'Shaughnessy, University of Wollongong, Australia

Title: Bootstrap inference in the longitudinal data with multiple sources of variation

Abstract: Linear mixed models allow us to model the dependence among the responses by incorporating random effects. Such dependence inherent in the longitudinal data from a complex design can be from the clustering between subjects and the repeated measurements within the subject. When the underlying distribution is not fully specified, we consider a class of estimators defined by the Gaussian quasi-likelihood for normal-like response variable. Historically it is challenging to make inference about the variance components in the framework of mixed models. We propose a new weighted estimating equation bootstrap, which varies weight schemes for different parameter estimators. The performance of the weighted estimating equation bootstrap is empirically evaluated in the simulation studies, showing improved coverage and variance estimation for the variance component estimators under models with normal and non-normal distributions for random effects. The asymptotic properties will also be addressed and we apply this new bootstrap method to a longitudinal dataset in biology.

(This is a joint work with Professor Alan Welsh from the Australian National University.)