One- and Two-Sided Tolerance Intervals for General Balanced Mixed Models and Unbalanced One-Way Random Models

Liao, Chen‐Tuo; Lin, Tsung-Chih; Iyer, Hari

doi:10.1198/004017005000000102

Cited by 65 publications

(57 citation statements)

References 16 publications

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“…On the other hand, Weerahandi [15] presents generalized pivotal quantities (GPQs) and generalized confidence intervals (GCIs) to construct exact confidence regions for specific parameters containing nuisance parameters. The GCI estimation has been recently proven successful in the exact interval estimation like the bioequivalence study [16], the interlaboratory trials study [17], the construction of tolerance intervals [18,19], the multivariate analysis of variance [20]. The simulation studies presented in the above cited articles strongly support that the GCI approach provides an exact interval estimation in finite sample sizes.…”

mentioning

confidence: 52%

On the exact interval estimation for the difference in paired areas under the ROC curves

Liao

Liu

2006

Statistics in Medicine

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An important measure for comparison of accuracy between two diagnostic procedures is the difference in paired areas under the receiver operating characteristic (ROC) curves. Non-parametric and maximum likelihood methods have been proposed for interval estimation for the difference in paired areas under ROC curves. However, these two methods are asymptotic procedures and their performance in finite sample sizes has not been thoroughly investigated. We propose to use the concept of generalized pivotal quantities (GPQs) to construct an exact confidence interval for the difference in paired areas under ROC curves. A simulation study is conducted to empirically investigate the probability coverage and expected length of the three methods for various combinations of sample sizes, values of the area under the ROC curve and correlations. Simulation results demonstrate that the exact confidence interval based on the concept of GPQs provides not only sufficient probability coverage but also reasonable expected length. Numerical examples using published data sets illustrate the proposed method.

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mentioning

confidence: 52%

On the exact interval estimation for the difference in paired areas under the ROC curves

Liao

Liu

2006

Statistics in Medicine

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“…95%) thatˇ% (e.g. 99%) of the results provided by the sending laboratory method will fall within the calculated tolerance interval [49][50][51][52]. This interval could then be considered the acceptance limits for the transfer study.…”

Section: Acceptance Limitsmentioning

confidence: 98%

Methodologies for the transfer of analytical methods: A review

Rozet

Dewé

Ziemons

et al. 2009

Journal of Chromatography B

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“…The concept of fiducial inference was originally introduced by Fisher 27 and subsequently refined by Fraser 28 . In addition, Liao et al 25 described three general approaches for constructing FGPQs and demonstrated their usefulness by deriving some previously unknown GPQs and GCIs. Connections between GPQs and fiducial inference are also discussed.…”

Section: Introductionmentioning

confidence: 98%

“…Krishnamoorthy and Mathew 24 derived one-sided tolerance limits for the observable random variable and the unobservable random effect in a one-way random model with balanced as well as unbalanced data. Liao et al 25 further developed procedures for one-and two-sided tolerance intervals for general linear models in which there exists a set of independent scaled chi-squared random variables. Although GCIs do not always have exact frequentist coverage, a number of simulation studies reported in the literature appear to support the claim that coverage probabilities of GCIs are sufficiently close to their nominal value so that they are in fact useful procedures in practical applications.…”

Section: Introductionmentioning

confidence: 99%

Generalized confidence intervals for assessing process capability of multiple production lines

Shu

Cheng

2008

Quality & Reliability Eng

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Process capability indices (PCIs) have become popular as unit-less measures on whether a process is capable of reproducing items meeting the quality requirement. A reliable approach for testing process capability is to establish an interval estimate, for which we can assert that it contains the true PCI value with a reasonable degree of certainty. However, the construction of such an interval estimate is not trivial, since the distribution of the commonly used C pk index involves unknown parameters. In this paper, we adopt the concept of generalized confidence intervals and generalized pivotal quantities to derive the generalized lower confidence bounds for providing critical information on process performance. Two practical applications in the area of process capability were considered, they include (i) assessing whether a process under investigation is capable and (ii) providing the lowest performance of the manufacturing processes from several production lines or several suppliers for quality assurance. The applicability of the derived results is also illustrated with examples.

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One- and Two-Sided Tolerance Intervals for General Balanced Mixed Models and Unbalanced One-Way Random Models

Cited by 65 publications

References 16 publications

On the exact interval estimation for the difference in paired areas under the ROC curves

On the exact interval estimation for the difference in paired areas under the ROC curves

Methodologies for the transfer of analytical methods: A review

Generalized confidence intervals for assessing process capability of multiple production lines

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