Statistics and Data Science Seminar: "Two topics in the analysis of spatially indexed functional data"

Abstract: The talk will consist of two parts. In the first part, I will focus on the problem of testing if there has been a global cooling trend in the ionosphere. The test uses a custom regression model for functional, spatially indexed responses that are only partially observed. It has been conjectured over 30 years ago that greenhouse gases should radiate heat into space once they enter the ionosphere. This should result in its thermal contraction. The height of the ionosphere can be approximately measured only directly over a terrestrial observatory. These observatories are unevenly spaced and have operated over different time periods. I will explain how the data collected by them can be used to test the conjecture of the thermal contraction of the ionosphere.

In the second part of the talk, I will present theory for the spectral analysis of data that are functions defined on a regular spatial grid. Since spatial dependence is the main characteristic of such data, the commonly used Karhunen-Loeve expansions, suitable for iid functions, is no longer optimal. Optimality and other properties of the new expansion will be explained.

Host: Debashis Mondal