smoother

A smoother is a procedure that produces a smoother representation of data, a function, or an image by reducing noise or high-frequency variation. By balancing fidelity to observed values with a penalty on roughness, a smoother aims to reveal the underlying signal, trend, or structure. Smoothing is used across statistics, signal processing, econometrics, and computer graphics, often as a preprocessing step before modeling or visualization.

Smoothing methods can be linear or nonlinear and parametric or nonparametric. Common linear smoothers include moving-average and exponential smoothing, which assign weights to nearby observations; kernel smoothers use a kernel function, such as Gaussian, to weight points by distance. Nonlinear smoothers include locally weighted regression (LOESS/LOWESS) and smoothing splines, where a penalty on roughness controls the trade-off between fit and smoothness. In image processing, Gaussian blur and related filters serve as smoothing operators to reduce noise in images.

A key aspect is the choice of smoothing parameter, such as window width or bandwidth. Larger smoothing parameters yield smoother results but risk obscuring genuine features; smaller parameters retain detail but may leave noise. The appropriate level of smoothing depends on data characteristics, noise level, and the goals of analysis.

Smoothers are used for trend estimation in time series, density estimation, data visualization, and preparing inputs for subsequent modeling. They are not a substitute for proper modeling when interpretability of noise or features is important, but they help clarify structure in noisy data.