A modification of the Hartung-Knapp confidence interval on the variance component in two-variance-component models

Barbora Arendacká

Kybernetika (2007)

  • Volume: 43, Issue: 4, page 471-480
  • ISSN: 0023-5954

Abstract

top
We consider a construction of approximate confidence intervals on the variance component σ 1 2 in mixed linear models with two variance components with non-zero degrees of freedom for error. An approximate interval that seems to perform well in such a case, except that it is rather conservative for large σ 1 2 / σ 2 , was considered by Hartung and Knapp in [hk]. The expression for its asymptotic coverage when σ 1 2 / σ 2 → ∞ suggests a modification of this interval that preserves some nice properties of the original and that is, in addition, exact when σ 1 2 / σ 2 → ∞ . It turns out that this modification is an interval suggested by El-Bassiouni in [eb]. We comment on its properties that were not emphasized in the original paper [eb], but which support use of the procedure. Also a small simulation study is provided.

How to cite

top

Arendacká, Barbora. "A modification of the Hartung-Knapp confidence interval on the variance component in two-variance-component models." Kybernetika 43.4 (2007): 471-480. <http://eudml.org/doc/33872>.

@article{Arendacká2007,
abstract = {We consider a construction of approximate confidence intervals on the variance component $\sigma ^2_1$ in mixed linear models with two variance components with non-zero degrees of freedom for error. An approximate interval that seems to perform well in such a case, except that it is rather conservative for large $\sigma ^2_1/\sigma ^2,$ was considered by Hartung and Knapp in [hk]. The expression for its asymptotic coverage when $\sigma ^2_1/\sigma ^2\rightarrow \infty $ suggests a modification of this interval that preserves some nice properties of the original and that is, in addition, exact when $\sigma ^2_1/\sigma ^2\rightarrow \infty .$ It turns out that this modification is an interval suggested by El-Bassiouni in [eb]. We comment on its properties that were not emphasized in the original paper [eb], but which support use of the procedure. Also a small simulation study is provided.},
author = {Arendacká, Barbora},
journal = {Kybernetika},
keywords = {variance components; approximate confidence intervals; mixed linear model; approximate confidence intervals; mixed linear model},
language = {eng},
number = {4},
pages = {471-480},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A modification of the Hartung-Knapp confidence interval on the variance component in two-variance-component models},
url = {http://eudml.org/doc/33872},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Arendacká, Barbora
TI - A modification of the Hartung-Knapp confidence interval on the variance component in two-variance-component models
JO - Kybernetika
PY - 2007
PB - Institute of Information Theory and Automation AS CR
VL - 43
IS - 4
SP - 471
EP - 480
AB - We consider a construction of approximate confidence intervals on the variance component $\sigma ^2_1$ in mixed linear models with two variance components with non-zero degrees of freedom for error. An approximate interval that seems to perform well in such a case, except that it is rather conservative for large $\sigma ^2_1/\sigma ^2,$ was considered by Hartung and Knapp in [hk]. The expression for its asymptotic coverage when $\sigma ^2_1/\sigma ^2\rightarrow \infty $ suggests a modification of this interval that preserves some nice properties of the original and that is, in addition, exact when $\sigma ^2_1/\sigma ^2\rightarrow \infty .$ It turns out that this modification is an interval suggested by El-Bassiouni in [eb]. We comment on its properties that were not emphasized in the original paper [eb], but which support use of the procedure. Also a small simulation study is provided.
LA - eng
KW - variance components; approximate confidence intervals; mixed linear model; approximate confidence intervals; mixed linear model
UR - http://eudml.org/doc/33872
ER -

References

top
  1. Arendacká A., Approximate confidence intervals on the variance component in a general case of a two-component model, In: Proc. ROBUST 2006 (J. Antoch and G. Dohnal, eds.), Union of the Czech Mathematicians and Physicists, Prague 2006, pp. 9–17 
  2. Billingsley P., Convergence of Probability Measures, Wiley, New York 1968 Zbl0944.60003MR0233396
  3. Boardman T. J., Confidence intervals for variance components – a comparative Monte Carlo study, Biometrics 30 (1974), 251–262 (1974) Zbl0286.62055
  4. Burdick R. K., Graybill F. A., Confidence Intervals on Variance Components, Marcel Dekker, New York 1992 Zbl0755.62055MR1192783
  5. El-Bassiouni M. Y., Short confidence intervals for variance components, Comm. Statist. Theory Methods 23 (1994), 7, 1951–1933 (1994) Zbl0825.62194MR1281896
  6. Hartung J., Knapp G., Confidence intervals for the between group variance in the unbalanced one-way random effects model of analysis of variance, J. Statist. Comput. Simulation 65 (2000), 4, 311–323 Zbl0966.62044MR1847242
  7. Park D. J., Burdick R. K., Performance of confidence intervals in regression models with unbalanced one-fold nested error structures, Comm. Statist. Simulation Computation 32 (2003), 3, 717–732 Zbl1081.62540MR1998237
  8. Seely J., El-Bassiouni Y., Applying Wald’s variance component test, Ann. Statist. 11 (1983), 1, 197–201 (1983) Zbl0516.62028MR0684876
  9. Tate R. F., Klett G. W., Optimal confidence intervals for the variance of a normal distribution, J. Amer. Statist. Assoc. 54 (1959), 287, 674–682 (1959) Zbl0096.12801MR0107926
  10. Thomas J. D., Hultquist R. A., Interval estimation for the unbalanced case of the one-way random effects model, Ann. Statist. 6 (1978), 3, 582–587 (1978) Zbl0386.62057MR0484702
  11. Tukey J. W., Components in regression, Biometrics 7 (1951), 1, 33–69 (1951) 
  12. Wald A., A note on the analysis of variance with unequal class frequencies, Ann. Math. Statist. 11 (1940), 96–100 (1940) MR0001502
  13. Wald A., A note on regression analysis, Ann. Math. Statist. 18 (1947), 4, 586–589 (1947) Zbl0029.30703MR0023498
  14. Williams J. S., A confidence interval for variance components, Biometrika 49 (1962), 1/2, 278–281 (1962) Zbl0138.13101MR0144424

NotesEmbed ?

top

You must be logged in to post comments.