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Technometrics Volume 47, 2005 - Issue 3
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Primary Article

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

C. T Liao Division of Biometry, Institute of Agronomy, National Taiwan University, Taipei, Taiwan
,
T. Y Lin Division of Biometry, Institute of Agronomy, National Taiwan University, Taipei, Taiwan
&
H. K Iyer Department of Statistics, Colorado State University, Fort Collins, CO 80523
Pages 323-335 | Published online: 01 Jan 2012

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Wei-Hwa Wu & Hsin-Neng Hsieh. (2022) Assessing the non-inferiority of a new treatment in a three-arm trial with unknown coefficient of variation. Communications in Statistics - Simulation and Computation 0:0, pages 1-18.
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Bernard G. Francq, Dan Lin & Walter Hoyer. (2020) Confidence and Prediction in Linear Mixed Models: Do Not Concatenate the Random Effects. Application in an Assay Qualification Study. Statistics in Biopharmaceutical Research 12:3, pages 262-272.
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Dharini Pathmanathan & S. H. Ong. (2014) A Monte Carlo simulation study of two-sided tolerance intervals in balanced one-way random effects model for non-normal errors. Journal of Statistical Computation and Simulation 84:11, pages 2329-2344.
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Gaurav Sharma & Thomas Mathew. (2012) One-Sided and Two-Sided Tolerance Intervals in General Mixed and Random Effects Models Using Small-Sample Asymptotics. Journal of the American Statistical Association 107:497, pages 258-267.
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RichardA. Lewis & StevenJ. Novick. (2012) A Generalized Pivotal Quantity Approach to the Parametric Tolerance Interval Test for Dose Content Uniformity Batch Testing. Statistics in Biopharmaceutical Research 4:1, pages 28-36.
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David Hoffman. (2010) One-Sided Tolerance Limits for Balanced and Unbalanced Random Effects Models. Technometrics 52:3, pages 303-312.
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Lanju Zhang, Thomas Mathew, Harry Yang, K. Krishnamoorthy & Iksung Cho. (2009) Tolerance Limits for a Ratio of Normal Random Variables. Journal of Biopharmaceutical Statistics 20:1, pages 172-184.
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Jen-pei Liu, Li-tien Lu & C. T. Liao. (2009) Statistical Inference for the Within-Device Precision of Quantitative Measurements in Assay Validation. Journal of Biopharmaceutical Statistics 19:5, pages 763-778.
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Hsiuying Wang & Fugee Tsung. (2009) Tolerance Intervals With Improved Coverage Probabilities for Binomial and Poisson Variables. Technometrics 51:1, pages 25-33.
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R. Romero-Villafranca, L. Zúnica, R. Romero-Zúnica & J. A. Pagura. (2008) One-sided tolerance limits for unbalanced one-way random effects models: a generalized Mee and Owen procedure. Journal of Statistical Computation and Simulation 78:12, pages 1215-1227.
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Miguel Fonseca, Thomas Mathew, João Tiago Mexia & Roman Zmyślony. (2007) Tolerance intervals in a two-way nested model with mixed or random effects. Statistics 41:4, pages 289-300.
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Meng-Chih Lee, Wei-Ya Wu, Hung-Yi Lu, Hsin-Neng Hsieh & Wei-Hwa Wu. (2023) Conducting the non-inferiority test for the means with unknown coefficient of variation in a three-arm trial. BMC Medical Research Methodology 23:1.
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K. Krishnamoorthy & Thomas Mathew. 2014. Wiley StatsRef: Statistics Reference Online. Wiley StatsRef: Statistics Reference Online.
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Jinadasa Gamage, Thomas Mathew & Samaradasa Weerahandi. (2013) Generalized prediction intervals for BLUPs in mixed models. Journal of Multivariate Analysis 120, pages 226-233.
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Mark A Gamalo, Saman Muthukumarana, Pulak Ghosh & Ram C Tiwari. (2011) A generalized p -value approach for assessing noninferiority in a three-arm trial . Statistical Methods in Medical Research 22:3, pages 261-277.
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T. Saffaj, B. Ihssane, F. Jhilal, H. Bouchafra, S. Laslami & S. Alaoui Sosse. (2013) An overall uncertainty approach for the validation of analytical separation methods. The Analyst 138:16, pages 4677.
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Haochuan Zhou & Gengsheng Qin. (2012) Confidence intervals for the difference in paired Youden indices. Pharmaceutical Statistics 12:1, pages 17-27.
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Jia-Ren Tsai & Chen-Tuo Liao. (2011) Method comparison on confidence interval construction for the slope in a linear measurement model with heteroscedastic errors. Journal of Chemometrics 25:9, pages 506-513.
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K. Krishnamoorthy & Fang Xie. (2011) Tolerance intervals for symmetric location-scale families based on uncensored or censored samples. Journal of Statistical Planning and Inference 141:3, pages 1170-1182.
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Rendao Ye, Tiefeng Ma & Songgui Wang. (2009) Generalized confidence intervals for the process capability indices in general random effect model with balanced data. Statistical Papers 52:1, pages 153-169.
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K. Krishnamoorthy & Yin Lin. (2010) Confidence limits for stress–strength reliability involving Weibull models. Journal of Statistical Planning and Inference 140:7, pages 1754-1764.
Crossref
Shein-Chung ChowChen-Tuo Liao & Chi-Rong Li. 2010. Encyclopedia of Biopharmaceutical Statistics. Encyclopedia of Biopharmaceutical Statistics 547 549 .
Chien‐Wei Wu, Ming‐Hung Shu & Feng‐Tsung Cheng. (2008) Generalized confidence intervals for assessing process capability of multiple production lines. Quality and Reliability Engineering International 25:6, pages 701-716.
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Steven Novick, David Christopher, Monisha Dey, Svetlana Lyapustina, Michael Golden, Stefan Leiner, Bruce Wyka, Hans-Joachim Delzeit, Chris Novak & Gregory Larner. (2009) A Two One-Sided Parametric Tolerance Interval Test for Control of Delivered Dose Uniformity. Part 1—Characterization of FDA Proposed Test. AAPS PharmSciTech 10:3.
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Jen‐pei Liu, Shein‐Chung Chow & Tsung‐Cheng Hsieh. (2009) Deviations from linearity in statistical evaluation of linearity in assay validation. Journal of Chemometrics 23:9, pages 487-494.
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E. Rozet, W. Dewé, E. Ziemons, A. Bouklouze, B. Boulanger & Ph. Hubert. (2009) Methodologies for the transfer of analytical methods: A review. Journal of Chromatography B 877:23, pages 2214-2223.
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Eric Hsieh, Chin‐fu Hsiao & Jen‐pei Liu. (2008) Statistical methods for evaluating the linearity in assay validation. Journal of Chemometrics 23:1, pages 56-63.
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T.Y. Lin & C.T. Liao. (2008) Prediction intervals for general balanced linear random models. Journal of Statistical Planning and Inference 138:10, pages 3164-3175.
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Tsai-Yu Lin, Chen-Tuo Liao & Hari K. Iyer. (2008) Tolerance intervals for unbalanced one-way random effects models with covariates and heterogeneous variances. Journal of Agricultural, Biological, and Environmental Statistics 13:2, pages 221-241.
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Bi-Min Hsu, Chien-Wei Wu & Ming-Hung Shu. (2007) Generalized confidence intervals for the process capability index C pm. Metrika 68:1, pages 65-82.
Crossref
Chi-Rong Li, Chen-Tuo Liao & Jen-Pei Liu. (2008) A non-inferiority test for diagnostic accuracy based on the paired partial areas under ROC curves. Statistics in Medicine 27:10, pages 1762-1776.
Crossref
Chi-Rong Li, Chen-Tuo Liao & Jen-Pei Liu. (2008) On the exact interval estimation for the difference in paired areas under the ROC curves. Statistics in Medicine 27:2, pages 224-242.
Crossref
B. M. Hsu, M. H. Shu & W. L. Pearn. (2006) Measuring process capability based on C pmk with gauge measurement errors . Quality and Reliability Engineering International 23:5, pages 597-614.
Crossref
Richard K. Burdick, Jorge Quiroz & Hariharan K. Iyer. (2006) The present status of confidence interval estimation for one-factor random models. Journal of Statistical Planning and Inference 136:12, pages 4307-4325.
Crossref
Samuel Kotz, Campbell B. Read, N. Balakrishnan, Brani Vidakovic & Norman L. JohnsonK. Krishnamoorthy & Thomas Mathew. 2004. Encyclopedia of Statistical Sciences. Encyclopedia of Statistical Sciences 1 23 .

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