Event Date
Speaker: Stanislav Volgushev (Associate Professor, Department of Statistical Sciences, University of Toronto)
Title: "Comparing many functional means"
Abstract: Many modern medical devices produce data with the structure of a multi-channel functional time series. Examples include medical imaging devices (fMRI, EEG, and ECG), high through-put time course gene sequencing devices, and high through-put devices that measure time-course microbiome composition. The typical number of channels can be of the same order or larger than the available sample size.
In this talk, we will present methodology to simultaneously test the equality of a growing number of functional means, in the example above, each mean corresponds to a channel. The number of channels can grow almost exponentially in the sample size. The proposed test is fully functional in the sense that we do not conduct any explicit dimension reduction or principal component analysis and is free of tuning parameters. The practical implementation is based on a Gaussian multiplier procedure and we provide explicit bounds on the speed of convergence of the rejection probability of our test to the nominal value under the null and discuss power against local alternatives. Our theoretical analysis leverages recent advances in high-dimensional Gaussian approximation but requires several intricate modifications of those techniques.
Bio: Stanislav Volgushev is currently associate professor and associate chair for graduate studies, in the Department of Statistical Sciences at the University of Toronto and Mathematical and Computational Sciences at the University of Toronto, Mississauga. Before joining the University of Toronto, he was Assistant Professor in Statistics at Cornell University and a visiting scholar at the University of Illinois at Urbana Champaign on a stipend from the DFG. He obtained his PhD at Ruhr University Bochum in 2010. His research interests are broadly in theoretical aspects of Statistics spanning a wide range of topics from quantile regression to dependence modeling via copulas, empirical process theory, time series and extreme value theory. He serves as Associate Editor for various major journals including the Electronic Journal of Statistics, Canadian Journal of Statistics and Scandinavian Journal of Statistics.
Faculty Website (links to Univ. Toronto): https://www.statistics.utoronto.ca/people/directories/all-faculty/stanislav-volgushev