Note that because the precise CI (13) depends on the nuisance parameter
[mu], this paper shows how to address the nuisance parameter
[mu] based on a generalized pivotal quantity, and an exact CI for [sigma] is proposed based on the generalized pivotal quantity.
In contrast, under the cause specific hazard rate framework  introduced a semiparametric Bayesian method assuming that each cumulative baseline cause-specific hazard rate function has a gamma prior distribution, and a marginal likelihood function based on data and the prior parameter values was proposed for the estimation of regression parameters by considering cumulative baseline cause-specific hazard rate functions as a nuisance parameter
This type of model arises when knowledge of all measurement variables is subject to significant error, and the model assumes a true value for each variable, which is to be estimated at least as a nuisance parameter
Optimal Tests When a Nuisance Parameter
Is Present Only under the Alternative.
Generally, we would like to make inferences on parameters of interest without reference to specific nuisance parameter
This nuisance parameter
represents some trait that might influence a systematist's choice of taxa and is expected to be similar in close relatives.
These latter parameters are usually referred to as nuisance parameters
To simplify the computation, we use the concentrated CRB theory in , which can discard the nuisance parameters
and only considers the interested ones, to calculate the CRB on the direction parameters.
We are interested primarily in estimating the association between A(t) and survival, [beta], while treating as nuisance parameters
the underlying hazard functions,
For our purposes, the distributions of the intervention parameters [Omega] are of greatest interest, while the other parameters ([Theta], [Phi], and the variance of [Epsilon]) are nuisance parameters
that complicate interpretation.
A regression of x on z recovers the nuisance parameters
Conditional maximum likelihood methods have the disadvantage that certain restrictive assumptions must be made about the nature of the nuisance parameters
or about the effect of other variables in the model.