The phrase "a pivotal quantity" is correct and usable in written English.
It can be used in statistical contexts to refer to a function of the data and parameters that has a distribution that does not depend on the parameters.
Example: "In the analysis, we identified a pivotal quantity that allowed us to construct confidence intervals for the parameter of interest."
Alternatives: "a crucial statistic" or "a key measure".
This is accomplished by using a tilting argument to construct a first approximation to a pivotal quantity, and then by using a version of Stein's identity and very weak expansions to determine the correction terms.
Another way of explaining the same idea invokes the notion of a pivotal quantity.
The argument can be run whenever we can construct a pivotal quantity like that or, equivalently, whenever we can express the statistical model as a functional model.
Traditional confidence intervals can be constructed when there is a pivotal quantity with a known distribution free of nuisance parameters.
The GCI method is based on a generalized pivotal quantity G[ 25, 27], which is a generalization of the usual pivot [ 34].
Because of how the above statistical model is set up, we can construct the pivotal quantity $\hat{\theta}(s) - \theta$.
This pivotal quantity in Bayesian model selection expresses the change of relative belief in both models after observing experimental data.
Exact confidence intervals for a proportion of total variance, based on pivotal quantities, only exist for mixed linear models having two variance components.
Generalized confidence intervals (GCIs) introduced by Weerahandi [1993. Generalized confidence intervals (Corr: 94V89 p726). J. Am. Statist. Assoc. 88, 899 905] are based on generalized pivotal quantities (GPQs) and can be constructed for a much wider range of models.
Finally, we give one example and the Monte Carlo simulation to assess the behaviors of these pivotal quantities for establishing prediction intervals of the jth future observation (Y j), n − s < j ⩽ n).
Hence, we use these WMEs, approximate maximum likelihood estimator (AMLE) and best linear unbiased estimator (BLUE) of scale parameter to find pivotal quantities and obtain the prediction intervals of the jth future observation (Y j), n − s < j ⩽ n) based on the above censored sample.
