A0850
Title: Multi-resolution spatial methods on the sphere
Authors: HaoYun Huang - National Dong Hwa University (Taiwan) [presenting]
Abstract: Spatial prediction is investigated on the sphere in the presence of measurement errors, where data may be irregularly located. A special class of basis functions are first developed in the thin-plate-spline (TPS) function space on the sphere. These basis functions are ordered according to their level of smoothness from large-scale features to small-scale details, providing a multi-resolution representation and an orthogonal transformation of the data. Theoretically, it is shown that the number of basis functions selected by the conditional Akaike information criterion is small, and the resulting reduced-rank estimate achieves a good convergence rate to the target function. In addition, a multi-resolution mixed-effects spatial model is developed on the sphere by including a Gaussian spatial process to capture fine-scale information. Since large-scale features are captured by leading basis functions, the small-scale spatial process tends to have a short spatial dependence range, leading to a universal kriging estimate that allows rapid computations. A simulation experiment is performed, and an application to global sea-surface-temperature data observed from a satellite is given to demonstrate the effectiveness of the proposed method.
