Efficient multiresolution spatial predictions for large data arrays

Imputations of missing values and optimal smoothing with massive data arrays poses a computational challenge since ordinary kriging becomes infeasible. Imputation and smoothing with standard algorithms like inverse distance weighted nearest neighbour interpolation (IDW) and interpolation on triangulated irregular networks (TIN/IP) fail to incorporate the spatial structure and ignore information beyond the neighbourhood. Multiresolution spatial models (MRSM) or approximate kriging methods adapted to handling massive data sets can be expected to do better than IDW and TIN/IP in terms of mean square errors of prediction (MSEP). We illustrate a MRSM that is efficient, computationally fast, and easy to implement. In two forestry examples with imputation of LiDAR range values the MRSM achieved a lower MSEP than IDW, TIN/IP, and fixed ranked kriging. MRSM appear as especially attractive for the construction of a DTM from last return LiDAR pulses. A third example demonstrates MRSM for efficient smoothing.