Modeling of Sparse and Spatially Correlated Functional Data

• Activity Number: 87
• Type: Invited
• Date/Time: Sunday, August 3, 2014 : 8:30 PM to 10:30 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Surajit Ray*+ and Chong Liu and Giles Hooker
• Companies: University of Glasgow and State Street Global Advisors and Cornell University
• Keywords: Spatial Correlation ; Functional Data Analysis ; Spatio-temporal data ; Isotropy

Abstract

This work proposes a new method of estimating spatial correlation and reconstructing individual curve for correlated sparse functional data. The proposed method extends the Principal Analysis by Conditional Estimation (PACE) framework described by Yao and Muller in 2005. In particular, assuming spatial stationarity, cross-covariance surfaces are estimated for given spatial separation vectors using local linear smoothing. Raw between-curve correlations are estimated as the ratio of eigenvalues of the smoothed covariance and cross-covariance surfaces. Anisotropy Matern family is assumed to model spatial correlations and its associated parameters are fitted based on raw correlations. Then functional principal component scores are estimated using conditional expectation where spatial correlations are taken into account. This estimation framework is illustrated with simulation studies and is applied to a remote sensing data set as an option of gap-filling missing data. In addition, two hypothesis tests are proposed to examine either the separability or isotropy effect of spatial correlation.