題目： Surface Functional Models

報告人：諶自奇   副教授(中南大學(xué)）

時間：2018年9月27日（星期四）10：30-11：20

地點(diǎn)：2511

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.

報告人簡介：諶自奇，中南大學(xué)副教授，碩士生導(dǎo)師；安德森癌癥研究中心博士后。2012年畢業(yè)于東北師范大學(xué)概率與數(shù)理統(tǒng)計專業(yè)，在Journal of the American Statistical Association等國際雜志上發(fā)表論文，且是Statistica Sinica， Scandinavion Journal of Statistics等雜志的審稿人；獲2014年吉林省優(yōu)秀博士學(xué)位論文，主持國家自然科學(xué)基金青年基金和面上基金各一項(xiàng)。

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