Nuisance parameter
In statistics, a nuisance parameter is any parameter which is unspecified[1] 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
Nuisance parameters are often 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.
Theoretical statistics
The general treatment of nuisance parameters can be broadly similar between frequentist and Bayesian approaches to theoretical statistics. It relies on an attempt to partition the
In some special cases, it is possible to formulate methods that circumvent the presences of nuisance parameters. The
Practical statistics
Practical approaches to statistical analysis treat nuisance parameters somewhat differently in frequentist and Bayesian methodologies.
A general approach in a frequentist analysis can be based on maximum
In
See also
References
- ISBN 978-1-111-79878-9.
- Basu, D. (1977), "On the Elimination of Nuisance Parameters," Journal of the American Statistical Association, vol. 77, pp. 355–366.
- Bernardo, J. M., Smith, A. F. M. (2000) Bayesian Theory. Wiley. ISBN 0-471-49464-X
- Cox, D.R., Hinkley, D.V. (1974) Theoretical Statistics. Chapman and Hall. ISBN 0-412-12420-3
- Spall, J. C. and Garner, J. P. (1990), “Parameter Identification for State-Space Models with Nuisance Parameters,” IEEE Transactions on Aerospace and Electronic Systems, vol. 26(6), pp. 992–998.
- Young, G. A., Smith, R. L. (2005) Essentials of Statistical Inference, CUP. ISBN 0-521-83971-8