Sentence examples for pivotal quantity from inspiring English sources

The GCI method is based on a generalized pivotal quantity G[ 25, 27], which is a generalization of the usual pivot [ 34].

Another way of explaining the same idea invokes the notion of a pivotal quantity.

Because of how the above statistical model is set up, we can construct the pivotal quantity $\hat{\theta}(s) - \theta$.

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.

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.

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.

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.

They then construct generalised confidence intervals about the TDI estimate that are based on replacing parameters involved in Lin's [ 10] TDI expression with generalised pivotal quantities.

It must be noted that other instruments such as pivotal quantities [ 71] or different proper scoring rules [ 28] can be used if the calculations are done with MCMC methods (e.g. using WinBUGS [ 55, 72]).