eiparametriset

Eiparametriset, commonly translated as nonparametric methods, refer to a class of statistical techniques that do not assume a fixed parametric form for the underlying population distribution. They are used when the data do not meet the assumptions of parametric models, when the sample size is small, or when the measurement scale is ordinal or otherwise not suitable for parameter estimation.

Key features of eiparametriset methods include flexibility and fewer distributional assumptions. They often rely on ranks or order rather than raw values, which makes them robust to outliers and applicable to ordinal data. Some methods are distribution-free, while others require only weak conditions such as independence. Nonparametric approaches can be more computationally intensive, but modern computing has mitigated this issue.

Common examples of eiparametriset techniques include hypothesis tests like the Wilcoxon rank-sum test (Mann-Whitney U test), the Kruskal-Wallis test, and rank correlations such as Spearman’s rho and Kendall’s tau. In estimation, bootstrapping and permutation tests are widely used nonparametric tools. Nonparametric regression methods, such as kernel smoothing and LOESS, provide flexible fits without assuming a specific functional form. Even density estimation can be approached nonparametrically, for instance through kernel density estimation.

Applications of eiparametriset methods span many fields, including social sciences, biology, and economics, particularly when data do not satisfy parametric assumptions or when interpretability of a parametric model is limited. The trade-off is often efficiency: nonparametric methods can require larger samples to achieve the same precision as correctly specified parametric models. In Finnish statistical usage, the term eiparametriset is used interchangeably with nonparametric.