Editing Statistical inference (section)

=== Degree of models/assumptions ===
Statisticians distinguish between three levels of modeling assumptions:

* '''[[Parametric model|Fully parametric]]''': The probability distributions describing the data-generation process are assumed to be fully described by a family of probability distributions involving only a finite number of unknown parameters.<ref name="Cox20062" /> For example, one may assume that the distribution of population values is truly Normal, with unknown mean and variance, and that datasets are generated by [[Simple random sample|'simple' random sampling]]. The family of [[Generalized linear model#Model components|generalized linear models]] is a widely used and flexible class of parametric models.
* '''[[Nonparametric statistics#Non-parametric models|Non-parametric]]''': The assumptions made about the process generating the data are much less than in parametric statistics and may be minimal.<ref>van der Vaart, A.W. (1998) ''Asymptotic Statistics''  Cambridge University Press. {{isbn|0-521-78450-6}} (page 341)</ref> For example, every continuous probability distribution has a median, which may be estimated using the sample median or the [[Hodges–Lehmann estimator|Hodges–Lehmann–Sen estimator]], which has good properties when the data arise from simple random sampling.
* '''[[Semiparametric model|Semi-parametric]]''': This term typically implies assumptions 'in between' fully and non-parametric approaches. For example, one may assume that a population distribution has a finite mean. Furthermore, one may assume that the mean response level in the population depends in a truly linear manner on some covariate (a parametric assumption) but not make any parametric assumption describing the variance around that mean (i.e. about the presence or possible form of any [[heteroscedasticity]]). More generally, semi-parametric models can often be separated into 'structural' and 'random variation' components. One component is treated parametrically and the other non-parametrically. The well-known [[Cox model]] is a set of semi-parametric assumptions.{{citation needed|date=November 2023}}