Smoothing with the Best Rectangle Window is Optimal for All Tapered Rectangle Windows
This work provides a theoretical foundation for window selection in smoothing problems, but it is incremental as it builds on existing concepts in optimization and signal processing.
The paper tackles the problem of optimal weight window selection for weighted least squares, showing that the best rectangle window is optimal for tapered rectangle windows, and extends these results to least absolutes and arbitrary loss functions.
We investigate the optimal selection of weight windows for the problem of weighted least squares. We show that weight windows should be symmetric around its center, which is also its peak. We consider the class of tapered rectangle window weights, which are nonincreasing away from the center. We show that the best rectangle window is optimal for such window definitions. We also extend our results to the least absolutes and more general case of arbitrary loss functions to find similar results.