12
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

Exact tests and confidence intervals for ratio of variance components in unbalanced two-and three-stage nested designs

Pages 1197-1230 | Published online: 27 Jun 2007

Bibliography

  • Broemeling , L.D. 1969 . Confidence regions for variance ratios of random models . J. Amer. Statist , 64 : 660 – 664 .
  • Broemeling , L.D. 1978 . Simultaneous inferences for variance ratios of some mixed linear models . Commun, Statist.-Theor. Meth , A7 : 297 – 305 .
  • Gaylor , D.W. 1974 . Variance component testing in unbalanced nested designs . J. Amer. Statist. Assoc , 69 : 765 – 771 .
  • Davies , R.B. 1980 . Algrorithm AS155:The distribution of a linear combination of x2random variabl . Applied Statistics , 29 : 323 – 333 .
  • Farebrother , R.W. 1981 . Algorithm AS153. Pan's procedure for the tail probabilities of the Durbin-Watson statistic . Applied Statistics , 30 : 189 – 227 .
  • Farebrother , R.W. 1984a . The distribution of a linear combination of central x2random variables. A remark on AS153-Pan's procedure for the tail probabilities of the Durbin-Watson statistic . Applied Statistics , 33 : 363 – 366 .
  • Farebrother , R.W. 1984b . A remark on algorithms AS106, AS153 and AS155. The distribution of a linear combination of x2random variables . Applied Statistics , 33 : 366 – 369 .
  • Battese , G.E. 1973 . Transformations for estimation of linear models with nested-error structure . J. Amer. Statist. Assoc , 68 : 626 – 632 .
  • Graybill , F.A. 1976 . “ Theory and Application of the Linear Model ” . In North Scituate , Duxbury Press .
  • Wang , C.M. 1979 . Confidence intervals for proportions of variability in two-factor nested variance components models . J. Amer. Statist. Assoc , 74 : 368 – 374 .
  • Fenech , A.P. 1985 . Confidence intervals for a variance ratio, or for heritability, in an unbalanced mixed linear model . Biometrics , 41 : 137 – 152 .
  • Herbach , L.H. 1959 . Properties of model II type analysis of variance tests, A. Optimum nature of the F-test for model II in the balanced case . Ann. Math. Statist , 30 : 939 – 959 .
  • Imhof , J.P. 1962 . Computing the distribution of quadratic forms in normal variables . Biometrika , 49 : 284 – 426 .
  • Khuri , A.I. 1981 . Simultaneous confidence intervals for functions of variance components in random models . J. Amer. Statist. Assoc , 76 : 878 – 885 .
  • Khuri , A.I. 1982 . Direct products:a powerful tool for the analysis of balanced data . Commun. Statist. Theor.-Meth , A11 : 2903 – 2920 .
  • Abrahamse , A.P.J. 1969 . “ On the theory and application of the general linear mod ” . Rotterdam : Rotterdam University Press .
  • Kruskal , W.H. 1968 . Note to Tietjen and Moore (1968) article . Biometrics , 24 : 1025 – 1026 .
  • Lamotte , L.R. 1972 . Notes on the covariance matrix of a random nested ANOVA model . Ann. Math. Statist , 43 : 659 – 682 .
  • Lehmann , E.L. “ Testing statistical hypotheses ” . New York : John Wiley and Sons .
  • Mostafa , M.G. 1967 . Note on testing hypotheses in an unbalanced random effects model . Biometrika , 54 : 659 – 662 .
  • Neudecker , H. 1968 . The Kronecker matrix product and some of its applications in econometrics . Statistica Neerlandica , 22 : 69 – 82 .
  • Pincus , R. 1977 . On tests in variance components model . Math. Qperationsforsch.Statist. Series Statistics , 8 : 251 – 255 .
  • Rao , C.R. 1973 . Linear statistical inference and its applications , New York : John Wiley and Sons, Inc .
  • Roebruck , P. 1982 . On the optimality of F-test on variance com ponents in mixed linear models . Biometrical Journal , 24 : 811 – 815 .
  • Sahai , H. and Anderson , R.L. 1973 . Confidence regions for variance ratios of random models for balanced data . J. Amer. Statist. Assoc , 68 : 951 – 952 .
  • Satterthwaite , F.E. 1946 . An approximate distribution of estimates of variance components . Biometrics Bulletin , 2 : 110 – 114 .
  • Searle , S.R. 1971 . “ Linear Models ” . New York : John Wiley and Sons, Inc .
  • Seely , J.F. and El-Bassiouni , Y. 1983 . Applying Wald's variance component test . Ann. Statist , 11 : 197 – 201 .
  • Spjotvoll , E. 1966 . A mixed model in the analysis of variance, Optimal properties . Skandinayisk Aktuarietidskrift , 49 : 1 – 38 .
  • Spjotvoll , E. 1967 . Optimum invariant tests in unbalanced variance component models . Ann. Hath. Statist , 38 : 422 – 428 .
  • Spjotvoll , E. 1968 . Most powerful tests for some non-exponential families . Ann. Math. Statist , 39 : 772 – 784 .
  • Tan , W.Y. and Cheng , S.S. 1984 . On testing variance components in three-stages unbalanced nested random effects mode . Sankhya , 46 : 188 – 200 .
  • 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 .
  • Thompson , W.A. 1955 . On the ratio of variances in the mixed incomplete block model . Ann. Math. Statist , 26 : 721 – 733 .
  • Tietjen , G.L. 1974 . Exact and approximate tests for unbalanced random effects designs . Biometrics , 30 : 573 – 581 .
  • Tietjen , G.L. and Moore , R.H. 1968 . On testing significance of components of variance in the unbalanced nested analysis of variance . Biometrics , 24 : 423 – 429 .
  • Tong , L.Y. 1979 . Counterexamples to a result of Broemeling on simultaneous inferences for variance ratios of some mixed linear models . Commun. Statist.-Theor. Meth , A8 : 1197 – 1204 .
  • Verdooren , L.R. 08 1974 . “ Exact tests about variance ratios in unbalanced two and three stages nested designs ” . In Contributed paper 8th International Biometric Conference 08 , 25 – 30 . Constanta, Romania
  • Verdooren , L.R. 1976 . “ Exact confidence interval for the variance ratio in nested designs ” . In Compstat 1976 , Edited by: Gordesch , J. and Naeve , P. 221 – 228 . Wien : Phvsica-Verlag .
  • Verdooren , L.R. 1982 . How large is the probability for the estimate of a variance component to be negativ . Biometrical Journal , 24 : 339 – 360 .
  • Wald , A. 1940 . A note on the analysis of variance with unequal class frequencies . Ann. Math. Statist , 11 : 96 – 100 .
  • Wald , A. 1947 . A note on regression analysis . Ann. Math. Statist , 18 : 586 – 589 .
  • Wang , C.M. and Graybill , F.A. 1981 . Confidence intervals on a ratio of variances in the two-factor nested components of variance mode . Commun. statist.-ineor. Meth , A10 : 1357 – 1368 .
  • Yassaee , H. 1976 . “ Probability integral of inverted Dirichlet distribution and its applications ” . In Compstat 1976 , Edited by: Gordesch , J. and Naeve , P. 64 – 71 . Wien : Physica Verlag .
  • Yassaee , H. 1981 . On integrals of Dirichlet distributions and their applications . Commun. Statist.-Theor. Meth , A10 : 897 – 906 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.