Interval estimation of variance ratio in non-normal unbalanced one-way random models

References

• D.G. Bonett, Sample size requirements for estimating intraclass correlations with desired precision, Stat. Med. 21 (2002), pp. 1331–1335. doi: 10.1002/sim.1108
   PubMed Web of Science ®Google Scholar
• W.G. Cochran, Sampling Techniques, 3rd ed., Wiley Series in Probability and Mathematical Statistics-Applied, John Wiley & Sons, New York, 1977.
   Google Scholar
• A. Wald, A note on the analysis of variance with unequal class frequencies, Ann. Math. Statist. 11 (1940), pp. 96–100. doi: 10.1214/aoms/1177731946
   Google Scholar
• D.A. Harville and A.P. Fenech, Confidence intervals for a variance ratio, or for heritability, in an unbalanced mixed linear model, Biometrics 41 (1985), pp. 137–152.
   Google Scholar
• R.K. Burdick, F. Maqsood, and F.A. Graybill, Confidence intervals on the intraclass correlation in the unbalanced one-way classification, Comm. Statist. Theory Methods 15 (1986), pp. 3353–3378. doi: 10.1080/03610928608829315
   Web of Science ®Google Scholar
• J.D. Thomas and R.A. Hultquist, Interval estimation for the unbalanced case of the one-way random effects model, Ann. Statist. 6 (1978), pp. 582–587. doi: 10.1214/aos/1176344202
   Web of Science ®Google Scholar
• T. Zoubeidi and M.Y. El-Bassiouni, Sequential confidence intervals for variance components in one-way random models, J. Statist. Plann. Inference 137(4) (2007), pp. 1185–1198. doi: 10.1016/j.jspi.2006.04.004
   Web of Science ®Google Scholar
• M.Y. El-Bassiouni and T. Zoubeidi, Adaptive interval estimation in one-way random effects models, J. Statist. Plann. Inference 138 (2008), pp. 857–872. doi: 10.1016/j.jspi.2007.02.008
   Web of Science ®Google Scholar
• D.A. Harville, Maximum likelihood approaches to variance components estimation and to related problems, J. Amer. Statist. Assoc. 72 (1977), pp. 320–332. doi: 10.1080/01621459.1977.10480998
   Web of Science ®Google Scholar
• B.D. Burch and I.R. Harris, Closed-form approximations to the REML estimator of a variance ratio (or heritability) in a mixed linear model, Biometrics 57(4) (2001), pp. 1148–1156.
   Google Scholar
• J. Jiang, REML estimation: Asymptotic behavior and related topics, Ann. Statist. 24 (1996), pp. 255–286. doi: 10.1214/aos/1033066209
   Web of Science ®Google Scholar
• J. Jiang, Partially observed information and inference about non-Gaussian mixed linear models, Ann. Statist. 33(6) (2005), pp. 2695–2731. doi: 10.1214/009053605000000543
   Web of Science ®Google Scholar
• J. Hannig, H. Iyer, and P. Patterson, Fiducial generalized confidence intervals, J. Amer. Statist. Assoc. 101(473) (2006), pp. 254–269. doi: 10.1198/016214505000000736
   Web of Science ®Google Scholar
• E. Lidong, J. Hannig and H. Iyer, Fiducial intervals for variance components in an unbalanced two-component normal mixed linear model, J. Amer. Statist. Assoc. 103(482) (2008), pp. 854–865. doi: 10.1198/016214508000000229
   Web of Science ®Google Scholar
• J. Hannig, On generalized fiducial inference, Statist. Sinica 19(2) (2009), pp. 491–544.
   Web of Science ®Google Scholar
• R.K. Burdick, J. Quiroz, and H.K. Iyer, The present status of confidence interval estimation for one-factor random models, J. Statist. Plann. Inference 136(12) (2006), pp. 4307–4325. doi: 10.1016/j.jspi.2005.07.004
   Web of Science ®Google Scholar
• B.D. Burch, Assessing the performance of normal-based and REML-based confidence intervals for the intraclass correlation coefficient, Comput. Statist. Data Anal. 55 (2011), pp. 1018–1028. doi: 10.1016/j.csda.2010.08.007
   Web of Science ®Google Scholar
• B.D. Burch, Confidence intervals for variance components in unbalanced one-way random effects model using non-normal distributions, J. Statist. Plann. Inference 141 (2011), pp. 3793–3807. doi: 10.1016/j.jspi.2011.06.015
   Web of Science ®Google Scholar
• M. Shoukri, D. Tracy, and I. Mian, The effect of kurtosis in the estimation of the parameters of the one-way random effects model from familial data, Comput. Statist. Data Anal. 10(3) (1990), pp. 339–345. doi: 10.1016/0167-9473(90)90016-B
   Web of Science ®Google Scholar
• F. Teuscher, G. Herrendorfer, and V. Guiard, The estimation of skewness and kurtosis of random effects in the linear model, Biom. J. 36(6) (1994), pp. 661–672. doi: 10.1002/bimj.4710360603
   Web of Science ®Google Scholar
• H. Singh, S. Shukla, and S. Singh, The utilization of kurtosis in the estimation of the parameters of the one-way random effects model, Biom. J. 36(6) (2002), pp. 661–672.
   Google Scholar
• L. An and S. Ahmed, Improving the performance of kurtosis estimator, Comput. Statist. Data Anal. 52(5) (2008), pp. 2669–2681. doi: 10.1016/j.csda.2007.09.024
   Web of Science ®Google Scholar
• A. Olsen, J. Seely, and D. Birkes, Invariant quadratic unbiased estimation for two variance components, Ann. Statist. 4(5) (1976), pp. 878–890. doi: 10.1214/aos/1176343586
   Web of Science ®Google Scholar
• L.R. Lamotte, Invariant quadratic estimators in the random one-way ANOVA model, Biometrics 32 (1976), pp. 793–804. doi: 10.2307/2529265
   Web of Science ®Google Scholar
• S.R. Searle, G. Casella, and C.E. McCulloch, Variance Components, Wiley Series in Probability and Statistics, Wiley-Interscience [John Wiley & Sons], Hoboken, NJ, 2006. Reprint of the 1992 original, Wiley-Interscience Paperback Series.
   Google Scholar
• D.G. Bonett, Approximate confidence interval for standard deviation of nonnormal distributions, Comput. Statist. Data Anal. 50 (2006), pp. 775–782. doi: 10.1016/j.csda.2004.10.003
   Web of Science ®Google Scholar
• H. Ahrens and R. Pincus, On two measures of unbalancedness in a one-way model and their relation to efficency, Biom. J. 23 (1981), pp. 227–235. doi: 10.1002/bimj.4710230302
   Google Scholar
• S. Willie and S. Berman, Noaa national status and trends program eighth round intercomparison exercise results for trace metals in marine sediments and biological tissues, Technical report, NOAA Thech. Memorandum, NOS ORCA 83, 1995.
   Google Scholar
• P.H. Westfall, Robustness and power of tests for a null variance ratio, Biometrika 75 (1988), pp. 207–214. doi: 10.1093/biomet/75.2.207
   Web of Science ®Google Scholar
• R. Bhansali, L. Giraitis, and P. Kokoszka, Convergence of quadratic forms with nonvanishing diagonal, Statist. Probab. Lett. 77(7) (2007), pp. 726–734.
   Web of Science ®Google Scholar