A note on fiducial generalized pivots for in one-way heteroscedastic ANOVA with random effects

References

• Cochran , W. G. 1937 . Problems arising in the analysis of a series of similar experiments . J. R. Stat. Soc. , 49 : 102 – 118 .
   Google Scholar
• Iyer , H. K. , Wang , C. M.J. and Mathew , T. 2004 . Models and confidence intervals for true values in interlaboratory trials . JASA , 99 : 1060 – 1071 .
   Web of Science ®Google Scholar
• Wimmer , G. and Witkovský , V. 2003 . Between group variance component interval estimation for the unbalanced heteroscedastic one-way random effects model . J. Stat. Comput. Simul. , 73 : 333 – 346 .
   Web of Science ®Google Scholar
• Rao , P. S.R.S. , Kaplan , J. and Cochran , W. G. 1981 . Estimators for the one-way random effects model with unequal error variances . JASA , 76 : 89 – 97 .
   Web of Science ®Google Scholar
• Vangel , M. G. and Rukhin , A. L. 1999 . Maximum likelihood analysis for heteroscedastic one-way random effects ANOVA in interlaboratory studies . Biometrics , 55 : 129 – 136 .
   PubMed Web of Science ®Google Scholar
• Mathew , T. , Nahtman , T. , von Rosen , D. and Sinha , B. K. 2010 . Non-negative estimation of variance components in heteroscedastic one-way random-effects ANOVA models . Statistics , 44 ( 6 ) : 557 – 569 .
   Web of Science ®Google Scholar
• Hartung , J. and Knapp , G. 2005 . On confidence intervals for the among-group variance in the one-way random effects model with unequal error variances . J. Statist. Plann. Inference , 127 : 157 – 177 .
   Web of Science ®Google Scholar
• Li , X. 2007 . Comparison of confidence intervals on between group variance in unbalanced heteroscedastic one-way random models . Comm. Statist. Simulation Comput. , 36 : 381 – 390 .
   Web of Science ®Google Scholar
• Hannig , J. , Iyer , H. and Patterson , P. 2006 . Fiducial generalized confidence intervals . JASA , 101 : 254 – 269 .
   Web of Science ®Google Scholar
• Hannig , J. 2009 . On generalized fiducial inference . Statist. Sinica , 19 : 491 – 544 .
   Web of Science ®Google Scholar
• Thomas , J. D. and Hultquist , R. A. 1978 . Interval estimation for the unbalanced case of the one-way random effects model . Ann. Statist. , 6 : 582 – 587 .
   Web of Science ®Google Scholar
• Olsen , A. , Seely , J. and Birkes , D. 1976 . Invariant quadratic unbiased estimation for two variance components . Ann. Statist. , 4 : 878 – 890 .
   Web of Science ®Google Scholar
• El-Bassiouni , M. Y. 1994 . Short confidence intervals for variance components . Comm. Statist. Theory Methods , 23 : 1915 – 1933 .
   Web of Science ®Google Scholar
• Seely , J. 1977 . Minimal sufficient statistics and completeness for multivariate normal families . Sankhy¯a Ser. A , 39 : 170 – 185 .
   Google Scholar
• Rao , C. R. and Kleffe , J. 1988 . Estimation of Variance Components and Applications North-Holland, Amsterdam
   Google Scholar
• Seely , J. 1971 . “ Quadratic subspaces and completeness ” . In Ann. Math. Stat Vol. 42 , 710 – 721 .
   Google Scholar
• Park , D. J. and Burdick , R. K. 2003 . Performance of confidence intervals in regression models with unbalanced one-fold nested error structures . Comm. Statist. Simulation Comput. , 32 : 717 – 732 .
   Web of Science ®Google Scholar
• Arendacká , B. 2005 . Generalized confidence intervals on the variance component in mixed linear models with two variance components . Statistics , 39 : 275 – 286 .
   Web of Science ®Google Scholar
• Arendacká , B. 2007 . Fiducial generalized pivots for a variance component vs. an approximate confidence interval . Meas. Sci. Rev. , 6 ( 6 ) : 55 – 63 .
   Google Scholar
• Li , X. and Li , G. 2007 . Comparison of confidence intervals on the among group variance in the unbalanced variance component model . J. Stat. Comput. Simul. , 77 : 477 – 486 .
   Web of Science ®Google Scholar
• LaMotte , L. R. 1976 . Invariant quadratic estimators in the random, one-way ANOVA model . Biometrics , 32 : 793 – 804 .
   Web of Science ®Google Scholar