Multiscale local polynomial decompositions using bandwidths as scales

TheMultiscale Local Polynomial Transform (MLPT), developped in this paper, combines the benefits from local polynomial smoothing with sparse multiscale decompositions. The contribution of the paper is twofold. First, it focusses on the bandwidths used throughout the transform. These bandwidths operate as user controlled scales in a multiscale analysis, which is explained to be of particular interest in the case of nonequispaced data. The paper presents both a likelihood based optimal bandwidth selection and a fast, heuristic approach. The second contribution of the paper is the combination of local polynomial smoothing with orthogonal prefilters, similar to Daubechies’ wavelet filters, but defined on irregularly spaced covariate values.