Resampling methods for temporal and spatial processes and their higher order accuracy

Texas A&M Research Foundation, College Station TX

Investigators

Abstract

The project focuses on investigating higher order asymptotic properties of common resampling methods for time-series and spatial data and on development of new ones. Specifically, this project concentrates on (i) investigating higher order properties of resampling methods for infinite dimensional parameters of time series data; (ii) developing Edgeworth expansion theory for statistics under long range dependence; (iii) developing new resampling methods for spatial data on a regular grid with an aim towards achieving higher order accuracy, (iv) investigating ways to extend resampling methodology to irregularly spaced spatial data and study their higher order properties. Data exhibiting temporal and spatial dependence appear in many areas of sciences, such as Astronomy, Atmospheric Sciences, Economics, Geology, Hydrology, Physics, etc. Analyses of such data sets using current statistical methodology face some limitations. This is primarily due to the fact that the existing statistical methodology mostly rely on strong structural (i.e., parametric model) assumptions that are often inadequate to capture all important features of the data generating process. This project seeks to (i) develop new methodology (based on what are known as Resampling Methods) that provide valid assessment of uncertainty without strong structural assumptions and (ii) develop theoretical tools to investigate optimality properties of statistical methods for time- and space-dependent data.