Estimation theory

Nuisance parameter

In statistics, a nuisance parameter is any parameter which is unspecified 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 distributions, the variance(s), σ2 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, 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. (Wikipedia).

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Related pages

Scale parameter | Variance | Normal distribution | Likelihood-ratio test | Parameter | Markov chain Monte Carlo | Confidence interval | Debabrata Basu | Location–scale family | Linear regression | Likelihood function | Statistics | Ancillary statistic | Adaptive estimator | Regression dilution | Errors-in-variables models | Pivotal quantity