A Functional-Data Perspective in Spatial Data Analysis

Speaker: Tailen Hsing, University of Michigan

Abstract: More and more spatiotemporal data nowadays can be viewed as functional data. The first part of the talk focuses on the Argo data, which is a modern oceanography dataset that provides unprecedented global coverage of temperature and salinity measurements in the upper 2,000 meters of depth of the ocean. We discuss a functional kriging approach to predict temperature and salinity as a smooth function of depth, as well as a functional co-kriging approach of predicting oxygen concentration based on temperature and salinity data. The second part of the talk considers the nonparametric estimation of the spectral density of a spatial functional process. As is common in spatial statistics, the process is assumed to be observed at irregularly-spaced spatial locations. We propose a lag-window estimator and discuss its asymptotic properties, including optimality results assuming that the spectral density belongs to a certain class of functions.