Nuisance parameter

Any unknown parameter of a probability distribution in a statistical problem connected with the study of other parameters of a given distribution. More precisely, for a realization of a random variable , taking values in a sample space , , , suppose it is necessary to make a statistical inference about the parameters , . Then are nuisance parameters in the problem. For example, let be independent random variables, subject to the normal law , with unknown parameters and , and one wishes to test the hypothesis : , where is some fixed number. The unknown variance is a nuisance parameter in the problem of testing . Another important example of a problem with a nuisance parameter is the Behrens–Fisher problem. Naturally, for the solution of a statistical problem with nuisance parameters it is desirable to be able to make a statistical inference not depending on these parameters. In the theory of statistical hypothesis testing one often achieves this by narrowing the class of tests intended for testing a certain hypothesis in the presence of a nuisance parameter to a class of similar tests (cf. Statistical test).

References

[1]	Yu.V. Linnik, "Statistical problems with nuisance parameters" , Amer. Math. Soc. (1968) (Translated from Russian)

References

[a1]	E.L. Lehmann, "Testing statistical hypotheses" , Wiley (1978)
[a2]	E.L. Lehmann, "Theory of point estimation" , Wiley (1983)