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- W2100258049 abstract "This paper discusses a problem for recovering an underlying trend from noisy data. The key assumption is that the trend is monotonic, e.g., reflects accumulation of irreversible system deterioration. The trend is obtained as a maximum a posteriori probability estimate. The overall problem setup is related to <i xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>α</i> ‐ <i xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>β</i> filter and Hodrick-Prescott filter. The main difference is that instead of a Gaussian process noise, a one-sided exponentially distributed noise is assumed. The batch estimate is a solution to a Quadratic Programming problem. The approach works exceptionally well for piece-wise linear trends that have a small number of jumps in the trended variable or its increase rate. Theoretical analysis justifies the sparsity properties for the jumps in the solution." @default.
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- W2100258049 date "2007-07-01" @default.
- W2100258049 modified "2023-09-25" @default.
- W2100258049 title "Optimal Estimate of Monotonic Trend with Sparse Jumps" @default.
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- W2100258049 doi "https://doi.org/10.1109/acc.2007.4282395" @default.
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