A general technique for smoothing multi-dimensional datasets utilizing orthogonal expansions and lower dimensional smoothers

Smoothing methods are often used for discerning underlying patterns and structure concealed by statistical noise within a dataset. Adaptive smoothing approaches are particularly useful because the amount of smoothing imposed on the data is determined automatically from the statistical characteristics of subsets of the data itself. We show theoretically that an effective N-dimensional smoothing can be achieved by utilization of a series of non-identical n-dimensional (n