Approximate one-sided tolerance limits in random effects model and in some mixed models and comparisons

References

• Lyles RH, Kupper LL, Rappaport SM. Assessing regulatory compliance of occupational exposures via the balanced one-way random effects ANOVA model. J Agric Biol Environ Stat. 1997a;2:64–86. doi: 10.2307/1400641
   Google Scholar
• Lyles RH, Kupper LL, Rappaport SM. A lognormal distribution based exposure assessment method for unbalanced data. Ann Occup Hyg. 1997b;41:63–76.
   PubMed Web of Science ®Google Scholar
• Mee RW, Owen DB. Improved factors for one-sided tolerance limits for balanced one-way ANOVA random model. J Amer Statist Assoc. 1983;78:901–905. doi: 10.1080/01621459.1983.10477038
   Web of Science ®Google Scholar
• Beckman RJ, Tietjen GL. Two-sided tolerance limits for balanced random-effects ANOVA models (Correction: 1998, 40, p. 269). Technometrics. 1989;31:185–197. doi: 10.1080/00401706.1989.10488512
   Web of Science ®Google Scholar
• Bhaumik DK, Kulkarni PM. One-sided tolerance limits for unbalanced one-way ANOVA random effects model. Comm Statist Theory Methods. 1991;20:1665–1675. doi: 10.1080/03610929108830590
   Web of Science ®Google Scholar
• Vangel MG. New methods for one-sided tolerance limits for a one-way balanced random-effects ANOVA model. Technometrics. 1992;34:176–185. doi: 10.1080/00401706.1992.10484906
   Web of Science ®Google Scholar
• Liao C-T, Iyer HK. A tolerance interval for the normal distribution with several variance components. Statist Sinica. 2004;14:217–229.
   Web of Science ®Google Scholar
• Krishnamoorthy K, Mathew T. One-sided tolerance limits in balanced and unbalanced one-way random models based on generalized confidence limits. Technometrics. 2004;46:44–52. doi: 10.1198/004017004000000103
   Web of Science ®Google Scholar
• Liao C-T, Lin TY, Iyer HK. One- and two-sided tolerance intervals for general balanced mixed models and unbalanced one-way random models. Technometrics. 2005;47:323–335. doi: 10.1198/004017005000000102
   Web of Science ®Google Scholar
• Hoffman D. One-sided tolerance limits for balanced and unbalanced random effects models. Technometrics. 2010;52:303–312. doi: 10.1198/TECH.2010.09171
   Web of Science ®Google Scholar
• Krishnamoorthy K, Mathew T. Statistical tolerance regions: theory, applications and computation. Hoboken, NJ: Wiley; 2009.
   Google Scholar
• Zou GY, Donner A. Construction of confidence limits about effect measures: a general approach. Stat Med. 2008;27:1693–1702. doi: 10.1002/sim.3095
   PubMed Web of Science ®Google Scholar
• Zou GY, Taleban J, Huo CY. Simple confidence intervals for lognormal means and their differences with environmental applications. Environmetrics. 2009a;20:172–180. doi: 10.1002/env.919
   Web of Science ®Google Scholar
• Zou GY, Huo CY, Taleban J. Confidence interval estimation for lognormal data with application to health economics. Comput Statist Data Anal. 2009b;53:3755–3764. doi: 10.1016/j.csda.2009.03.016
   Web of Science ®Google Scholar
• Zou GY. Confidence interval estimation for the Bland-Altman limits of agreement with multiple observations per individual. Stat Methods Med Res. 2011;22:632–642. 10.1177/0962280211402548
   Web of Science ®Google Scholar
• Fonseca M, Mathew T, Mexia JT, Zmyslony R. Tolerance intervals in a two-way nested model with mixed or random effects. Statistics. 2007;41:289–300. doi: 10.1080/02331880701270648
   Web of Science ®Google Scholar
• Graybill FA, Wang CM. Confidence intervals on nonnegative linear combinations of variances. J Amer Statist Assoc. 1980;75:869–873. doi: 10.1080/01621459.1980.10477565
   Web of Science ®Google Scholar
• Thomas JD, Hultquist RA. Interval estimation for the unbalanced case of the one-way random effects model. Ann Statist. 1978;6:582–587. doi: 10.1214/aos/1176344202
   Web of Science ®Google Scholar
• Lee H-I, Liao C-T. Interval estimation for conformance proportions in a normal variance components models. J Qual Technol. 2012;44:63–79.
   Web of Science ®Google Scholar
• Ostle B, Mensing RW. Statistics in research: basic concepts and techniques for research workers. 3rd ed. Ames, IA: Iowa State University Press; 1975.
   Google Scholar
• Satterthwaite FE. An approximate distribution of estimates of variance components. Biom Bull. 1946;2:110–114. doi: 10.2307/3002019
   Google Scholar
• Krishnamoorthy K, Lian X. Closed-form approximate tolerance intervals for some general linear models and comparison studies. J Stat Comput Simul. 2012;82:547–563. doi: 10.1080/00949655.2010.545061
   Web of Science ®Google Scholar