Richard Samworth, Cambridge University

Professor Richard Samworth obtained his PhD in Statistics from the University of Cambridge in 2004, and has remained in Cambridge since, becoming a full professor in 2013 and the Professor of Statistical Science in 2017. Samworth currently holds a European Research Council Advanced Grant. His main research interests are in high-dimensional and nonparametric statistics, and has developed methods and theory for shape-constrained inference, data perturbation techniques (subsampling,the bootstrap, random projections, knockoffs), changepoint estimation,missing data and classification, amongst others. He received the COPSS Presidents' Award in 2018, gave an Institute of Mathematical Statistics (IMS) Medallion lecture (2018), and was awarded the Adams prize (2017). Samworth is an elected fellow of the American Statistical Association(2015) and the IMS (2014), and was awarded a Philip Leverhulme Prize(2014), the Royal Statistical Society (RSS) Guy Medal in Bronze (2012) and the RSS Research Prize (2008). He recently completed a three-year term as co-editor (with Ming Yuan) of the Annals of Statistics, and was elected a Fellow of the Royal Society in 2021.

**Title: Optimal nonparametric testing of Missing Completely**** ****At Random, and its connections to compatibility**

**Abstract**: Given a set of incomplete observations, we study the nonparametric problem of testing whether data are Missing Completely At Random (MCAR). Our first contribution is to characterise precisely the set of alternatives that can be distinguished from the MCAR null hypothesis. This reveals interesting and novel links to the theory of Fréchet classes (in particular, compatible distributions) and linear programming, and we leverage tools developed in these fields to propose MCAR tests that are consistent against all detectable alternatives. Moreover, we define a natural measure of ease of detectability (an incompatibility index), and exploit ideas from max-flow min-cut theory to prove that our tests achieve the optimal minimax separation rate according to this measure in certain cases.

Jane-Ling Wang, University of California, Davis

** **Dr. Jane-Ling Wang is Distinguished Professor of Statistics at the University of California, Davis. Her research areas include deep learning, functional data analysis, neuroimaging data analysis, semiparametric and nonparametric modeling approaches and survival analysis. She is interested in theory as well as applications, and has received the Noether Senior Research Award (2016), the ICSA Distinguished Achievement Award (2018) and the Humboldt Research Award (2020). She has been a co-editor of Statistica Sinica (2002-2005) and is currently a

co-editor of JASA Theory and Methods (since 2000).

**Title: The Three Faces of Functional Data**

**Abstract**: We consider functional data that are random functions on an interval, e.g. [0, 1], hence they can be viewed as stochastic processes. Functional data have become increasingly common due to advances in modern technology to collect and store such data. In reality these random functions can only be measured at discrete time grids and the measurement schedule may vary among subjects. Depending on the sampling frequency functional data are collected either intensively or sparsely, which affects both methodology and theory. Furthermore, the data may contain noise, a.k.a. measurement errors. In this talk, we review briefly how the different sampling plans and measurement errors have been handled in the literature and point out the challenges caused by sparse sampling designs that have only a few measurements per subject. Such sparsely observed functional data are ubiquitous in longitudinal studies and require special handling. We summarize the basic principle to tackle such data and show a few success stories. We then move to the recent discovery of a new challenge in testing homogeneity (equal distributions) for independent samples of functional data. We show why this is not feasible for sparsely observed functional data and propose a new approach of testing marginal homogeneity, i.e. that the marginal distributions are the same among the independent samples for all time points t. The pros and cons of such a marginal approach will be discussed as well as an interesting phenomenon that is unique to this approach. Both theory and numerical results will be presented.

Shurong Zheng, Northeast Normal University

Dr. Shurong Zheng is Professor of School of Mathematics and Statistics, Northeast Normal University, China. Her research interest is large dimensional random matrix theory and high-dimensional statistical inference. Now, she is an associate editor of Annals of Statistics, Statistica Sinica, Journal of Multivariate Analysis, Statistics and Probability Letters.

**Title: Spectral properties of high-dimensional sample correlation matrix and its applications**

**Abstract:** Sample correlation matrix plays an important role in multivariate statistical analysis, for example, in factor analysis, principal component analysis and etc. We study the limiting spectral distribution and central limit theorem (CLT) of linear spectral statistics of high-dimensional sample correlation matrix under the linear component structure and elliptical structure when the data dimension and sample size tend to infinity proportionally. The CLTs are used for high-dimensional testing problems of correlation matrix. Moreover, we study the convergence of the spike eigenvalues of high-dimensional sample correlation matrix and apply it to estimate the number of factors of high-dimensional factor models.