Abstract
Trend filtering is a modern approach to nonparametric regression that is more adaptive to local smoothness than splines or similar basis procedures. Existing analyses of trend filtering focus on estimating a function corrupted by homoskedastic Gaussian noise, but our work extends this technique to general exponential family distributions. This extension is motivated by the need to study massive, gridded climate data derived from polar-orbiting satellites. We present algorithms tailored to large problems, theoretical results for general exponential family likelihoods, and principled methods for tuning parameter selection without excess computation.
Funding Statement
DJM was partially supported by the National Sciences and Engineering Research Council of Canada (NSERC) grant RGPIN-2021-02618.
Acknowledgments
The authors would like to thank the anonymous referees, an Associate Editor and the Editor for their constructive comments that improved the quality of this paper.
Citation
Veeranjaneyulu Sadhanala. Robert Bassett. James Sharpnack. Daniel J. McDonald. "Exponential family trend filtering on lattices." Electron. J. Statist. 18 (1) 1749 - 1814, 2024. https://doi.org/10.1214/24-EJS2241
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