Optimal experimental design that minimizes the width of simultaneous confidence bands

We propose an optimal experimental design for a curvilinear regression model that minimizes the band-width of simultaneous confidence bands. Simultaneous confidence bands for curvilinear regression are constructed by evaluating the volume of a tube about a curve that is defined as a trajectory of a regression basis vector (Naiman, 1986). The proposed criterion is constructed based on the volume of a tube, and the corresponding optimal design that minimizes the volume of tube is referred to as the tube-volume optimal (TV-optimal) design. For Fourier and weighted polynomial regressions, the problem is formalized as one of minimization over the cone of Hankel positive definite matrices, and the criterion to minimize is expressed as an elliptic integral. We show that the Mobius group keeps our problem invariant, and hence, minimization can be conducted over cross-sections of orbits. We demonstrate that for the weighted polynomial regression and the Fourier regression with three bases, the tube-volume optimal design forms an orbit of the Mobius group containing D-optimal designs as representative elements.

举办单位：数学与统计学院

发 布 人：吴双 发布时间： 2018-08-02

发 布 人：吴双 发布时间： 2018-08-02

Satoshi Kuriki graduated from the Ueda High School. He got Bachelors and Ph.D. degrees from the Department of Mathematical Engineering and Instrumental Physics of the University of Tokyo in 1982 and 1993, respectively. He is now a professor of the Institute of Statistical Mathematics, Research Organization of Information and Systems (ISM, ROIS). He was serving as the General Section Chief Editor of the Annals of the Institute of Statistical Mathematics (AISM) during 2007-2012.