Glätttechniken

Glätttechniken, or smoothing techniques, are methods used to reduce random variation in data, signals, or images and to reveal underlying structure such as trends, cycles, or densities. They aim to produce a smoother representation without distorting essential features too much. They are widely used across statistics, econometrics, engineering and data science.

In statistics and data analysis, smoothing helps estimate functions, densities, or time-series signals when observations are noisy. In image and audio processing, smoothing reduces visual or auditory noise. In machine learning, smoothing can serve as a preprocessing step, as a denoising mechanism or to stabilize regression and classification models.

Common methods include time-series techniques such as moving average, exponential smoothing (including Holt-Winters), and Kalman smoothing; nonparametric approaches such as kernel smoothing (Nadaraya-Watson) and LOESS/LOWESS; and smoothing splines. In image and signal processing, Gaussian and other low-pass filters, median filters, and Fourier-domain filtering are used. Parametric approaches control bias-variance through a smoothing parameter; nonparametric methods adapt to data with less rigid assumptions.

Choosing a method involves considerations of bias, variance, and edge effects. The smoothing parameter, such as bandwidth or span, determines the extent of smoothing and can be selected by cross-validation or information criteria. Over-smoothing may erase important features; under-smoothing may leave noise; validation is essential.