21
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

Approximate confidence intervals on positive linear combinations of expected mean squares

Pages 81-96 | Received 01 Oct 1990, Published online: 27 Jun 2007

References

  • Abramowitz , M. and Stegun , I. A. 1965 . “ Applied Mathematics Series ” . In Handbook of Mathematical Functions , Washington D.C : U.S. Government Printing Office .
  • 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 .
  • Burdick , R. K. and Graybill , F. A. 1988 . The present status of confidence interval estimation on variance components in balanced and unbalanced random models . Communications in Statistics-Theory and Methods , 17 : 1165 – 1195 .
  • Burdick , R. K. and Sielken , R. L. 1978 . Exact confidence intervals for linear combinations of variance components in nested classification . Journal of theAmerican Statistical Association , 73 : 632 – 635 .
  • Fleiss , J. L. 1971 . On the distribution of a linear combination of independent chi squares . Journal of the American Statistical Association , 66 : 142 – 144 .
  • Graybill , F. A. and Wang , C. M. 1980 . Confidence intervals on nonnega-tive linear combinations of variances . Journal of the American Statistical Association , 75 : 869 – 873 .
  • IMSL Inc. (1987), The IMSL Math/Library, Houston, Texas
  • Johnson , N. L. and Kotz . 1972 . Distributions in Statistics: Continuous Multivariate Distributions , New York : John Wiley .
  • Lu , T. F. , Graybill , F. A. and Burdick , R. K. 1987 . Confidence intervals on the ratio of expected mean squares ----------- . Biometrics , 43 : 535 – 543 .
  • Satterthwaite , F. E. 1946 . An approximate distribution of estimates of variance components . Biometrics Bulletin , 2 : 110 – 114 .
  • J. F. 1980 . Some remarks on exact confidence intervals for positive linear combinations of variance components . Journal of the American Statistical Association , 75 : 372 – 374 .
  • Ting , N. , Burdick , R. K. , Graybill , F. A. and Gui , R. 1989 . One-sided confidence intervals on linear combinations of variance components . Statistics and Probability Letters , 8 : 129 – 135 .
  • Trickett , W. H. and Welch , B. L. 1954 . On the comparison of two means: further discussion of iterative methods for calculating tables . Biometrika , 41 : 361 – 374 .
  • Wang , C. M. 1988 . One-sided confidence intervals for the positive linear combination of two variances . Communications in Statistics-Simulation and Computation , 17 : 283 – 291 .
  • Welch , B. L. 1956 . On linear combinations of several variances . Journal of the American Statistical Association , 51 : 132 – 148 .

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.