nonparametric

Nonparametric refers to statistical methods that do not assume a specific parametric form for the underlying population distribution or function being estimated. In contrast to parametric methods, which specify a finite set of parameters (such as mean and variance of a normal distribution), nonparametric approaches aim to be flexible and rely less on prespecified models. They often make minimal distributional assumptions, and many are distribution-free under certain conditions.

Nonparametric methods are widely used for hypothesis testing, estimation, and density or regression problems. Classic nonparametric tests include the Mann–Whitney U test, the Wilcoxon signed-rank test, and the Kruskal–Wallis test, which compare groups without relying on normality. Spearman's rank correlation and Kendall's tau are nonparametric alternatives to Pearson correlation. In estimation, nonparametric density estimation (e.g., kernel density estimation) and nonparametric regression (e.g., kernel regression, locally weighted scatterplot smoothing) build models that adapt to data without a fixed parametric form.

Strengths of nonparametric methods include robustness to distributional misspecification and the ability to capture complex patterns. Limitations include reduced statistical efficiency when a parametric model is appropriate, higher data requirements, sensitivity to bandwidth or smoothing choices, and the curse of dimensionality in higher dimensions.