重磅 | 第九届中国人民大学国际统计论坛主报告预告（二）

Richard Samworth

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

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, that allow us to propose MCAR tests that are consistent against all detectable alternatives. We define an incompatibility index as a natural measure of ease of detectability, establish its key properties, and show how it can be computed exactly in some cases and bounded in others. Moreover, we prove that our tests can attain the minimax separation rate according to this measure, up to logarithmic factors. Our methodology does not require any complete cases to be effective, and is available in the R package MCARtest.

Richard Samworth is Professor of Statistical Science and Director of the Statistical Laboratory at the University of Cambridge. His main research interests are in high-dimensional and nonparametric statistics, and has developed methods and theory for data perturbation techniques (subsampling, the bootstrap, random projections, knockoffs), change point estimation, shape-constrained inference, missing data, (conditional) independence testing 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 served as co-editor of the Annals of Statistics from 2019-21, and was elected a Fellow of the Royal Society in 2021.