摘要: The two-sample inference for the population mean functions problem is one of the most fundamental research topics in functional data analysis. Projection-based testing has become popular in recent years, which constructs test statistic from the coefficient vectors obtained by projecting the functional observations into a finite dimensional space. In this paper, the loss of information due to projection is measured for the first time. Based on this, we give the most powerful projection function which brings no loss of information, and estimate it by a conjugate gradient algorithm. We also discuss choosing projection functions from datadriven functions, i.e. the principal components, where a new criterion of selecting a subset of eigenfunctions is proposed, and from known basis functions, such as B-Spline basis functions. In a simulation study we compare the performance of these projection functions.

简介：柏杨，上海财经大学统计与管理学院副教授（长聘），博士生导师；中国现场统计研究会资源与环境统计分会副理事长。柏杨博士一直从事纵向（函数型）数据分析等统计建模方法与理论的研究工作。目前在Statistica Sinica、Scandinavian Journal of Statistics、Journal of Multivariate Analysis等国际知名统计学期刊上发表论文20余篇，google学术他引150余次。已经主持完成国家自然科学基金面上项目和青年项目各一项，第三完成人获得教育部2014年度高等学校科学研究优秀成果奖二等奖1项。