报告题目：Series of Talks on Simultaneous Inference and Statistical Classification
Talk 1: Prediction and calibration for all future values: exact simultaneous tolerance intervals for linear regression
报 告 人：韩杨 副教授 （英国曼彻斯特大学）
报告时间：2024年7月7日 （星期日）下午14：00-15：00
报告地点：数学楼114（小报告厅）
邀 请 人：王晓光 副教授 联系电话：84708354
报告摘要：Statistical calibration using regression is a useful statistical tool with many applications. For confidence sets for x-values associated with infinitely many future y-values, there is a consensus in the statistical literature that the confidence sets constructed should guarantee a key property. While it is well known that the confidence sets based on the simultaneous tolerance intervals (STI's) guarantee this key property conservatively, it is desirable to construct confidence sets that satisfy this property exactly. Also, there is a misconception that the confidence sets based on the pointwise tolerance intervals (PTI's) also guarantee this property. This work constructs the weighted simultaneous tolerance intervals (WSTI's) so that the confidence sets based on the WSTI's satisfy this property exactly if the future observations have the x-values distributed according to a known specific distribution F(·). Through the lens of the WSTI's, convincing counter examples are also provided to demonstrate that the confidence sets based on the PTI's do not guarantee the key property in general and so should not be used.
报告人简介：Dr Yang Han is an Associate Professor / Senior Lecturer in Statistics in the Department of Mathematics at the University of Manchester in the UK. Her main research interests are simultaneous inference and multiple comparison procedures. She is a Fellow of the UK Higher Education Academy and a Fellow of the Royal Statistical Society. She has won a Distinguished Achievement Award for Teacher of the Year at the University of Manchester.
