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Published in:
2015 | OriginalPaper | Chapter
Discrete Prolate Spheroidal Sequences as Filters in Generalized Additive Models
Authors : Wesley S. Burr, Hwashin H. Shin
Published in: Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science
Publisher: Springer International Publishing
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Abstract
Air Health Indicator (AHI) is a joint Health Canada/Environment Canada initiative that seeks to model the Canadian national population health risk due to short-term (acute) effects of air pollution. The commonly accepted model in the field uses cubic spline-based temporal smoothers embedded in generalized additive models (GAMs) to account for seasonal and long-term variations in the response. From a spectral point of view, it is natural to think of these smooth, long-term variations as low-frequency components, and the temporal smoother as a linear filter.
Examining the frequency response of the filters typically used, we show that the performance leaves much to be desired. Adapting the discrete prolate spheroidal sequences as filters, taking inspiration from their similar use in the multitaper method, we are able to significantly improve the frequency response of the smoother. We conclude with a discussion of the implications for controlling bias from the long timescale structure of parametric covariates, and suggest a prefiltering stage to such models.