Abstract
\(L_\infty \) estimation is not part of the traditional canon in applied regression analysis; its use presupposes noise whose distribution has bounded support. However, there are applications where controlling the \(L_\infty \)-norm of residuals is very useful and thus including an \(L_\infty \) penalty on the residuals is warranted. In this paper, we will describe a method for computing such estimates using an iteratively reweighted least squares approach where the weights are defined by differential equations. An application of this method is given for total variation denoising, which is a commonly used method in signal and image processing for preserving sharp discontinuities in the underlying signal.
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Knight, K. (2019). A Continuous-Time Iteratively Reweighted Least Squares Algorithm for \(L_\infty \) Estimation. In: Steland, A., Rafajłowicz, E., Okhrin, O. (eds) Stochastic Models, Statistics and Their Applications. SMSA 2019. Springer Proceedings in Mathematics & Statistics, vol 294. Springer, Cham. https://doi.org/10.1007/978-3-030-28665-1_4
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DOI: https://doi.org/10.1007/978-3-030-28665-1_4
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