Idempotent One-Sided Approximation of Median Smoothers

Authors

Carl H. Rohwer

Year

1989

Journal Paper

Algorithm

Lulu Smoothing

Source

Journal of Approximation Theory

Identifiers

DOI 10.1016/0021-9045(89)90017-8

Abstract¶

There has been considerable interest recently in nonlinear smoothing algorithms for handling outliers in time series. The simpler algorithms are predominantly chosen to be rank-based selectors, and concatenations of these. Analytical investigation lags and is considered difficult, so that theoretical understanding seems inadequate. It may be that a lattice is a useful structure for investigating and comparing smoothers, and a few related simple selectors are defined and investigated for this purpose.

Summary¶

Introduces one-sided idempotent smoothers that bound and approximate median smoothers while being easier to analyze algebraically. The paper is an early step toward LULU theory, framing nonlinear time-series denoising through ordered lattice operators rather than only through running medians.