Southwest Jiaotong University School of Mathematics


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来源:   作者:     日期:2018-09-25 10:08:19   点击数:  

题目: Surface Functional Models

报告人:谌自奇   副教授(中南大学)



摘要:The aim of this paper is to develop a new framework of surface functional models for surface functional data which contains repeated observations in both the domains, (typically, time-location). The surface functional models are far beyond the multivariate functional models. The primary interest in our problem is to investigate the relationship between a response and the two domains, where the numbers of observations in both domains within a subject may be diverging. We estimate the mean function based on local linear smoothers because of their appealing empirical and theoretical properties. Unprecedented complexity presented in the surface functional models, such as possibly distinctive sampling designs and the dependence between the two domains, makes the theoretical investigation challenging.We are able to provide a comprehensive investigation of the asymptotic properties of the mean function estimatorbased on a general weighing scheme,   including   equal weight (EW) and subject-to-denseness weight (SDW), as special cases.Moreover, we can mathematically categorize the surface data into nine cases according to the sampling designs (sparse, dense, and ultra-dense) of both the domains, essentially based on the relative order of the number of  observations in each  domain to the sample size.We derive the specific asymptotic theories and optimal bandwidth orders in each of the nine sampling design cases under all the three weighing schemes.We also  examine the finite-sample performance of the estimators through simulation studies and an autism study involving white-matter fiber skeletons.

报告人简介:谌自奇,中南大学副教授,硕士生导师;安德森癌症研究中心博士后。2012年毕业于东北师范大学概率与数理统计专业,在Journal of the American Statistical Association等国际杂志上发表论文,且是Statistica Sinica Scandinavion Journal of Statistics等杂志的审稿人;获2014年吉林省优秀博士学位论文,主持国家自然科学基金青年基金和面上基金各一项。