Bootstrap inference for skew-normal unbalanced heteroscedastic one-way classification random effects model

References

• Krishnamoorthy K, Guo HZ. Assessing occupational exposure via the one-way random effects model with unbalanced data. J Stat Plan Inference. 2005;128(1):219–229.
   Web of Science ®Google Scholar
• Jose KK, Luke JA. Confidence intervals for process capability indices for the unbalanced one-way random effect ANOVA model. Qual Reliab Eng Int. 2012;28(4):371–375.
   Web of Science ®Google Scholar
• Meng SW, Xiao ZH. Credibility premium based on skew-normal random effect model. Stat Res. 2015;32(1):73–78.
   Google Scholar
• Jeyaratnam S, Othman AR. Test of hypothesis in one-way random effects model with unequal error variances. J Stat Comput Simul. 1985;21(1):51–57.
   Web of Science ®Google Scholar
• Weerahandi S. Testing variance components in mixed models with generalized p-values. J Am Stat Assoc. 1991;86(413):151–153.
   Web of Science ®Google Scholar
• Liu XH, Hu Y, Hu YQ. A new generalized confidence interval for the among-group variance in the heteroscedastic one-way random effects model. Commun Stat Simul Comput. 2015;46(3):2299–3110.
   Web of Science ®Google Scholar
• Jung I, Sen PK. Robust testing for random effects in unbalanced heteroscedastic one-way models. J Nonparametr Stat. 2008;20(4):305–317.
   Web of Science ®Google Scholar
• Zhang D, Davidian M. Linear mixed models with flexible distributions of random effects for longitudinal data. Biometrics. 2001;57(3):795–802.
   PubMed Web of Science ®Google Scholar
• Ghidey W, Lesaffre E, Eilers P. Smooth random effects distribution in a linear mixed model. Biometrics. 2004;60(4):945–953.
   PubMed Web of Science ®Google Scholar
• Ghosh P, Branco MD, Chakraborty H. Bivariate random effect model using skew-normal distribution with application to HIV-RNA. Stat Med. 2007;26(6):1255–1267.
   PubMed Web of Science ®Google Scholar
• Lachos VH, Dey DK, Cancho VG. Robust linear mixed models with skew-normal independent distributions from a Bayesian perspective. J Stat Plan Inference. 2009;139(12):4098–4110.
   Web of Science ®Google Scholar
• Lin TI, Lee JC. Estimation and prediction in linear mixed models with skew-normal random effects for longitudinal data. Stat Med. 2008;27(9):1490–1507.
   PubMed Web of Science ®Google Scholar
• Ye RD, Wang TH. Inferences in linear mixed models with skew-normal random effects. Acta Math Sin. 2015;31(4):576–594.
   Web of Science ®Google Scholar
• Ye RD, Xu LJ, Luo K, et al. A parametric bootstrap approach for one-way classification model with skew-normal random effects. Appl Math Ser B. 2019;34(4):423–435.
   Web of Science ®Google Scholar
• Ye RD, Qi J. Bootstrap inference of variance component function in skew-normal one-way classification random effect model. J Appl Stat Manag. 2022;41(2):309–321.
   Google Scholar
• Li XM, Li GY. Confidence intervals on sum of variance components with unbalanced designs. Commun Stat Theory Methods. 2005;34(4):833–845.
   Web of Science ®Google Scholar
• Li XM. Comparison of confidence intervals on between group variance in unbalanced heteroscedastic one-way random models. Commun Stat Simul Comput. 2007;36(2):381–390.
   Web of Science ®Google Scholar
• Ye RD, Ma TF, Luo K. Inferences on the reliability in balanced and unbalanced one-way random models. J Stat Comput Simul. 2014;84(5):1136–1153.
   Web of Science ®Google Scholar
• Ma TF, Wang SG. Test of variance components of linear mixed model. Appl Math Ser A. 2007;22(4):433–440.
   Google Scholar
• Zhao J, Wang SG, Wang L. Exact tests of variance components in nested error components regression model. Chinese J Appl Probab Stat. 2014;30(1):31–39.
   Google Scholar
• Zhao J, Cheng WH, Wu MX, et al. Generalized p-value tests of variance components in panel data model. Appl Math Ser A. 2014;29(2):171–179.
   Google Scholar
• Xu LW. Bootstrap statistical inference of complex data and its application. Beijing: Science Press; 2016.
   Google Scholar
• Krishnamoorthy K, Lu F, Mathew TA. A parametric bootstrap approach for ANOVA with unequal variances: fixed and random models. Comput Stat Data Anal. 2007;51(12):5731–5742.
   Web of Science ®Google Scholar
• Ma CX, Tian LL. A parametric bootstrap approach for testing equality of inverse gaussian means under heterogeneity. Commun Stat Simul Comput. 2009;38(6):1153–1160.
   Web of Science ®Google Scholar
• Xu LW, Tian MZ. Parametric bootstrap inferences for panel data models. Commun Stat Theory Methods. 2017;46(11):5579–5594.
   Web of Science ®Google Scholar
• Sinha SK. Bootstrap tests for variance components in generalized linear mixed models. Can J Stat. 2009;37(2):219–234.
   Web of Science ®Google Scholar
• Xu LW. Parametric bootstrap approaches for two-way MANOVA with unequal cell sizes and unequal cell covariance matrices. J Multivariate Anal. 2015;133:291–303.
   Web of Science ®Google Scholar
• Azzalini A, Dalla Valle A. The multivariate skew-normal distribution. Biometrika. 1996;83(4):715–726.
   Web of Science ®Google Scholar
• Azzalini A, Capitanio A. Statistical applications of the multivariate skew normal distribution. J R Stat Soc B. 1999;61(3):579–602.
   Google Scholar
• Yang FQ, Xu LW, Abula A. Parameter bootstrap test of variance component in one-way random effects model. Proceedings of Statistical Education and Applied Statistics Symposium; Beijing: China Commercial Publishing; 2012.
   Google Scholar
• Weerahandi S. Generalized confidence intervals. J Am Stat Assoc. 1993;88(423):899–905.
   Web of Science ®Google Scholar
• Wimmer G, Witkovsky V. Between group variance component interval estimation for the unbalanced heteroscedastic one-way random effects model. J Stat Comput Simul. 2003;73(5):333–345.
   Web of Science ®Google Scholar
• Arendacka B. Approximate interval for the between-group variance under heteroscedasticity. J Stat Comput Simul. 2012;82(2):209–218.
   Web of Science ®Google Scholar
• Ye RD, Luo K. Statistical inference of several mixed effect models. Beijing: Science Press; 2016.
   Google Scholar
• Wu MX, Tian Y, Liu AY. Robust inference in linear mixed model with skew normal-symmetric error. Front Math China. 2017;12(6):1483–1500.
   Web of Science ®Google Scholar
• Wu MX, Zhao J, Wang TH, et al. The ANOVA-type inference in linear mixed model with skew-normal error. J Syst Sci Complex. 2017;30(3):710–720.
   Web of Science ®Google Scholar
• Genton MG. Discussion of ‘the skew-normal’. Scand J Stat. 2005;32(2):189–198.
   Web of Science ®Google Scholar