nonparametrisch

Nonparametric methods are statistical techniques that do not assume a specific parametric form for the population distribution or the functional relationship under study. The term contrasts with parametric methods, which specify a fixed set of parameters and a presumed distribution shape, such as normal or exponential families. In nonparametric analysis, inferences rely on the data itself rather than on strong distributional assumptions.

Common uses include hypothesis testing, distribution estimation, and regression without assuming normality or constant variance. Examples of nonparametric tests are the Wilcoxon rank-sum test, the Mann-Whitney U test, the Kruskal-Wallis test, and the Friedman test. Correlation can be assessed with rank-based measures such as Spearman's rho or Kendall's tau. Density estimation and function estimation can be performed with kernel methods, histograms, splines, or local polynomial regression.

Key considerations include trade-offs in statistical efficiency, sample size requirements, and interpretability. Nonparametric methods are typically more robust to model misspecification and outliers, but they can be less powerful than correctly specified parametric methods and may require larger samples. They also often involve tuning choices (for example, bandwidth in kernel methods) that affect performance.

Beyond classical statistics, nonparametric ideas influence machine learning and econometrics. Algorithms such as k-nearest neighbors, decision trees, and kernel-based methods are considered nonparametric, as they do not assume a fixed functional form. In practice, analysts may combine parametric and nonparametric components, yielding semi-parametric approaches that aim to balance flexibility with interpretability.