The present status of confidence interval estimation on variance components in balanced and unbalanced random models

References

• Arteaga , C. , Jeyaratnam , S. and Graybill , F.A. 1982 . Confidence intervals for proportions of total variance in the two-way cross component of variance model . Comm. Statist. - Theor. Meth , 11 : 1643 – 1658 .
   Web of Science ®Google Scholar
• Bartlett , M.S. 1953 . Approsimate confidence intervals II.More than one unknown parameter . Biometrika , 40 : 306 – 317 .
   Web of Science ®Google Scholar
• Boardman , T.J. 1974 . Confidence intervals for variance components a comparative Monte Carlo study . Biometrics , 30 : 251 – 262 .
   Web of Science ®Google Scholar
• Broemeling , I.D. 1969a . Confidence intervals for measures of heritability . Biometrics , 25 : 424 – 427 .
   PubMed Web of Science ®Google Scholar
• Broemeling , I.D. 1969b . Confidence regions for variance ratios of random models . J. Axner, Statist. Assoc , 64 : 660 – 664 .
   Web of Science ®Google Scholar
• Broemeling , L.D. 1976 . Simultaneous inference & for variance ratios of some mixed linear mode . Comm. Statist. - Theor. Meth , A7 : 297 – 305 .
   Google Scholar
• Broemeling , L.D. and Bee , D.E. 1976 . Simultaneous confidence intervals for parameters of a balanced incomplete block . J. Amer. Statist. Assoc , 71 : 425 – 428 .
   Web of Science ®Google Scholar
• Bulmer , M.G. 1957 . Approximate confidence limits for components of variance . Biometrika , 44 : 159 – 167 .
   Web of Science ®Google Scholar
• Burdick , R.K. , Birch , N.J. and Graybill , F.A. 1986 . Confidence intervals on measures of variability in an unbalanced two-fold nested design with equal subsampli . J. Statist. Comput. Simul. , 25 : 259 – 272 .
   Google Scholar
• Burdick , R.K. and Eickman , J.E. 1986 . Confidence intervals on the among group variance component in the unbalanced one-fold nested design . J. Statist. Comput. Simul , 26 : 205 – 219 .
   Google Scholar
• Burdick , R.K. and Graybill , F.A. 1985 . Confidence intervals on the total variance in an unbalanced two-fold nested classification with equal subsampling . Comm. Statist. - Theor. Meth , 14 : 761 – 774 .
   Web of Science ®Google Scholar
• Burdick , R.K. and Graybill , F.A. 1984 . Confidence intervals on linear combinations of variance components in the unbalanced one-way classification . Technometrics , 26 : 131 – 136 .
   Web of Science ®Google Scholar
• Burdick , R.K. , Graybill , F.A. and Maqsood , F. 1986 . Confidence intervals on the intraclass correlation in the unbalanced one-way classification . Comm. Statist.-Theor. Meth , 15 : 3353 – 3378 .
   Web of Science ®Google Scholar
• Burdick , R.K. and Sielken , R.L. Jr. 1978 . Exact confidence intervals for linear combinations of variance components in nested classifications . J. Amer. Statist. Assoc , 73 : 632 – 635 .
   Web of Science ®Google Scholar
• Davenport , James M. 1975 . Two methods of estimating the degrees of freedom of an approximate . Biometrika , 62 : 682 – 684 .
   Web of Science ®Google Scholar
• Donner , A. and Wells , G. 1986 . A comparison of confidence interval methods for the intraclass correlation coefficie . Biometrics , 42 : 401 – 412 .
   PubMed Web of Science ®Google Scholar
• Fenech A.P. Harville D.A. Confidence regions for variance components in unbalanced mixed linear models 1986 Unpublished paper
   Google Scholar
• Graybill , F.A. 1961 . An I n t roduetion to Statistica1 Models , New York : McGraw-Hill .
   Google Scholar
• Graybill , F.A. 1976 . Theory and Application of the Linear Model , North Scituate, Massachusetts : Duxbury .
   Google Scholar
• Graybill , F.A. and Wang , C.M. 1979 . Confidence intervals for proportions of variability in two-factor nested variance component models . J. Amer.Statist. Assoc , 74 : 368 – 374 .
   Web of Science ®Google Scholar
• Graybill , F.A. and Wang , C.M. 1980 . Confidence intervals on nonnegative linear combinations of variances . J. Amer. Statist, Assoc , 75 : 869 – 873 .
   Web of Science ®Google Scholar
• Guenther , W.C. 1977 . Calculation of factors for tests and confidence intervals concerning the ratio of two normal variances . Amer. Statist , 31 : 175 – 177 .
   Web of Science ®Google Scholar
• Harville , D.A. and Fenech , A.P. 1985 . Confidence intervals for a variance ratio, or for heritability, in an unbalanced mixed linear model . Biometrics , 41 : 137 – 152 .
   PubMed Web of Science ®Google Scholar
• Healy , W.C. Jr. 1961 . Limits for a variance component with an exact confidence coefficient . Ann. Math. Statist , 32 : 466 – 476 .
   Google Scholar
• Howe , W.C. 1974 . Approximate confidence limits on the mean of X+Y where X and Y are two tabled independent random variabl . J. Amer, Statist. Assoc , 69 : 789 – 794 .
   Web of Science ®Google Scholar
• Huitson , A. 1955 . A method of assigning confidence limits to linear combinations of variances . Biometrika , 42 : 471 – 479 .
   Web of Science ®Google Scholar
• Jeyaratnam S. Inference in linear models with dependent error structure Colorado State University Fort Collins, Colorado 1978 Unpublished dissertation
   Google Scholar
• Jeyaratnam , S. and Graybill , F.A. 1980 . Confidence intervals on variance components in three-factor cross-classification models . Technometrics , 22 : 375 – 380 .
   Web of Science ®Google Scholar
• Khuri , A.I. 1981 . Simultaneous confidence intervals for functions of variance components in random mode . J. Amer. Statist. Assoc , 76 : 878 – 885 .
   Google Scholar
• Khuri , A.I. and Sahai , Hardeo . 1985 . Variance Components Analysis:A Selective Literature Survey . Int. Stat, Rev , 53 : 279 – 300 .
   Web of Science ®Google Scholar
• Leiva , Richado A. and Graybill , F.A. 1986 . Confidence intervals for variance components in the balanced two-way model with interactions . Comm. Statist. - SimuU Cnmput , 15 : 301 – 322 .
   Web of Science ®Google Scholar
• V , K.J. and Narula , S.C. 1974 . Shortest confidence intervals for the ratio of two normal varianc . Canad. J. Statist , 2 : 83 – 87 .
   Google Scholar
• Lu T.-F.C Confidence intervals on sums, differences and ratios of variance components Colorado State University Fort Collins, Colorado 1985 Unpublished dissertation
   Google Scholar
• Lu , T.-F.C. , Graybill , F.A. and Burdick , R.K. 1987a . “ Confidence intervals on a difference of expected mean squares, Forthcoming in ” . In J. Statist. Planning and Inference
   Google Scholar
• Lu T.-F.C Graybill F.A. Burdick R.K. Confidence intervals on the ratio of expected mean squares (θ₁+dθ₂)/θ₃ 1987b Forthcoming in Biometrics
   Google Scholar
• Lu T.-F.C Graybill F.A. Burdick R.K. Confidence intervals on the ratio of expected mean squares (θ₁-dθ₂)/θ₃) 1987c Paper in review
   Google Scholar
• Moriguti , S. 1954 . Confidence limits for a variance component . Rep. Statist, Appl. Res,, Juse , 3 : 7 – 19 .
   Google Scholar
• Sahai , H. 1974 . Simultaneous confidence intervals for variance components in some balanced random effects models . Sankhya, Ser , B 36 : 278 – 287 .
   Google Scholar
• Sahai , H. 1979 . A Bibliography on Variance Components . Int. Stat. Rev , 47 : 177 – 222 .
   Google Scholar
• Sahai , H. and Anderson , R.L. 1973 . Confidence regions for variance ratios of random models for balanced da . J. Amer. Statist. Assoc , 68 : 951 – 952 .
   Web of Science ®Google Scholar
• Sahai , H. , Khuri , A. and Kapadia , C.H. 1985 . A second bibliography on variance componen . Comm. Statist. - Theor. Meth , 14 : 63 – 115 . Al, R2
   Web of Science ®Google Scholar
• Statterthwaite , F.E. 1941 . Synthesis of vaiance . Psychometrika , 6 : 309 – 316 .
   Google Scholar
• Satterthwaite , F.E. 1946 . An approximate distribution of estimates of variance components . Biom, Bull , 2 : 110 – 114 .
   Google Scholar
• Seeiy , J. 1980 . Some remarks on exact confidence intervals for positive linear combinations of variance componen . J. Amer. Statist. Assoc , 75 : 372 – 374 .
   Google Scholar
• Seely , J.F. and El-Bassiouni , Y. 1983 . Applying Wald's variance component test . Ann. Statist , 11 : 197 – 201 .
   Web of Science ®Google Scholar
• Smith , D.W. and Murray , L.W. 1984 . An alternative to Eisenhart's Model II and mixed model in the case of negative variance estimates . J. Amer. Statist. Assoc , 79 : 145 – 151 .
   Web of Science ®Google Scholar
• Smith , H.F. 1936 . The problem of comparing the results of two experiments with unequal errors . J. of the Council of Scientific and Industrial Research , 9 : 211 – 212 .
   Google Scholar
• Spjotvoll , E. 1968 . Confidence intervals and test for variance ratios in unbalanced variance components models . Rev. Internat. Statist. Inst , 36 : 37 – 42 .
   Google Scholar
• Srinivasan Syamaia Confidence intervals on functions of variance components in unbalanced two-way design models Colorado State University Fort Collinsj, Colorado 1986 Unpublished dissertation
   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
• Thompson , W.A. Jr. 1955a . The ratio of variances in a variance components model . Ann. Math. Statist , 26 : 325 – 329 .
   Google Scholar
• Thompson , W.A. Jr. 1955b . On the ratio of variances in the mixed incomplete block model . Ann. Math. Statist , 26 : 721 – 733 .
   Google Scholar
• Thomsen , I.B. 1975 . Testing hypotheses in unbalanced variance components models for two-way layouts . Ann, Statist , 3 : 257 – 265 .
   Web of Science ®Google Scholar
• Tukey , J.W. 1951 . Components in regression . Biometrics , 7 : 33 – 69 .
   PubMed Web of Science ®Google Scholar
• Verdooren , L.R. 1976 . Exact confidence interval for the variance ratio in nested designs . COMPSTAT , 7 : 221 – 228 . Second Symposium on Computational Statist
   Google Scholar
• Wald , A. 1940 . A note on nanlysis of variance with unequal class frequencies . Ann. Math. Statist , 11 : 96 – 199 .
   Google Scholar
• Wald , A. 1947 . A note on regression analysis . Ann. Math. Statist , 18 : 586 – 589 .
   Google Scholar
• Wang C.M. Confidence intervals on functions of vaiance components Colorado State University Fort Collins, Colorado 1978 Unpublished dissertation
   Google Scholar
• Wang , C.M. and Graybill , F.A. 1981 . Confidence intervals on a ratio of variances in the two-factor nested components of variance model . Comm. Statist.- Theor. Meth , 10 : 1357 – 1368 .
   Web of Science ®Google Scholar
• Welch , B.L. 1956 . On linear combinations of several variances . J. Amer. Statist. Assoc , 51 : 132 – 148 .
   Web of Science ®Google Scholar
• Williams , J.S. 1962 . A confidence interval for variance components . Biometrika , 49 : 278 – 281 .
   Web of Science ®Google Scholar