A0748
Title: Inverse regression for spatially distributed functional data
Authors: Suneel Babu Chatla - University of Texas at El Paso (United States) [presenting]
Ruiqi Liu - Texas Tech University (United States)
Abstract: Spatially distributed functional data are prevalent in many statistical applications. Given their complex and high-dimensional nature, functional data often require dimension-reduction methods to extract meaningful information. Inverse regression is one such approach that has become very popular in the past two decades. We study the inverse regression in the framework of functional data observed at irregularly positioned spatial sites. The functional predictor is the sum of a spatially dependent functional effect and a spatially independent functional nugget effect, while the relation between the scalar response and the functional predictor is modeled using the inverse regression framework. The domain-expanding infill (DEI) framework is discussed for spatial asymptotics, which is a mix of the traditional expanding domain and infill frameworks. The DEI framework overcomes the limitations of traditional spatial asymptotics in the existing literature. Under this unified framework, asymptotic theory is developed, and conditions that are necessary for the estimated eigen-directions to achieve optimal rates of convergence are identified. The asymptotic results include pointwise and L2 convergence rates.
