Editing Statistical classification (section)

==Frequentist procedures==

Early work on statistical classification was undertaken by [[Ronald Fisher|Fisher]],<ref>{{Cite journal |doi = 10.1111/j.1469-1809.1936.tb02137.x|title = The Use of Multiple Measurements in Taxonomic Problems|year = 1936|last1 = Fisher|first1 = R. A.|journal = [[Annals of Eugenics]]|volume = 7|issue = 2|pages = 179–188|hdl = 2440/15227|hdl-access = free}}</ref><ref>{{Cite journal |doi = 10.1111/j.1469-1809.1938.tb02189.x|title = The Statistical Utilization of Multiple Measurements|year = 1938|last1 = Fisher|first1 = R. A.|journal = [[Annals of Eugenics]]|volume = 8|issue = 4|pages = 376–386|hdl = 2440/15232|hdl-access = free}}</ref> in the context of two-group problems, leading to [[Fisher's linear discriminant]] function as the rule for assigning a group to a new observation.<ref name=G1977>Gnanadesikan, R. (1977) ''Methods for Statistical Data Analysis of Multivariate Observations'', Wiley. {{ISBN|0-471-30845-5}} (p. 83&ndash;86)</ref> This early work assumed that data-values within each of the two groups had a [[multivariate normal distribution]]. The extension of this same context to more than two groups has also been considered with a restriction imposed that the classification rule should be [[linear]].<ref name=G1977/><ref>[[C. R. Rao|Rao, C.R.]] (1952) ''Advanced Statistical Methods in Multivariate Analysis'', Wiley. (Section 9c)</ref> Later work for the multivariate normal distribution allowed the classifier to be [[nonlinear]]:<ref>[[T. W. Anderson|Anderson, T.W.]] (1958) ''An Introduction to Multivariate Statistical Analysis'', Wiley.</ref> several classification rules can be derived based on different adjustments of the [[Mahalanobis distance]], with a new observation being assigned to the group whose centre has the lowest adjusted distance from the observation.