Editing Nuisance parameter (section)

{{Short description|Statistical parameter needed for a model but not of primary interest}}

In [[statistics]], a '''nuisance parameter''' is any [[parameter]] which is unspecified<ref>{{Cite book |last1=Wackerly |first1=Dennis |url=https://books.google.com/books?id=lTgGAAAAQBAJ&dq=wackerly+math+stats&pg=PP1 |title=Mathematical Statistics with Applications |last2=Mendenhall |first2=William |last3=Scheaffer |first3=Richard L. |date=2014-10-27 |publisher=Cengage Learning |isbn=978-1-111-79878-9 |language=en}}</ref> but which must be accounted for in the hypothesis testing of the parameters which are of interest. 

The classic example of a nuisance parameter comes from the [[normal distribution]], a member of the [[location–scale family]]. For at least one normal distribution, the [[variance]](s), ''σ<sup>2</sup>'' is often not specified or known, but one desires to hypothesis test on the mean(s).  Another example might be [[linear regression]] with unknown variance in the [[explanatory variable]] (the independent variable): its variance is a nuisance parameter that must be accounted for to derive an accurate [[interval estimate]] of the [[regression slope]], calculate [[p-values]], hypothesis test on the slope's value; see [[regression dilution]].

Nuisance parameters are often [[scale parameter|scale parameters]], but not always; for example in [[errors-in-variables models]], the unknown true location of each observation is a nuisance parameter. A parameter may also cease to be a "nuisance" if it becomes the object of study, is estimated from data, or known.