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Title: Surface functional models Authors:  Ziqi Chen - Central South University (China) [presenting]
Abstract: The aim is to develop a new framework of surface functional models for surface functional data which contains repeated observations in two domains (typically, time-location). The primary problem of interest 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. The surface functional models are far beyond the multivariate functional models with two-dimensional predictor variables. 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 of the resulting estimator challenging. We provide a comprehensive investigation of the asymptotic properties of the local linear estimator of the mean function based on a general weighting scheme, including equal weight (EW), direction-to-denseness weight (DDW) and subject-to-denseness weight (SDW), as special cases.