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

Kybernetika (2007)

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

## Access Full Article

top## Abstract

top## How to cite

topArendacká, 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- 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
- Billingsley P., Convergence of Probability Measures, Wiley, New York 1968 Zbl0944.60003MR0233396
- Boardman T. J., Confidence intervals for variance components – a comparative Monte Carlo study, Biometrics 30 (1974), 251–262 (1974) Zbl0286.62055
- Burdick R. K., Graybill F. A., Confidence Intervals on Variance Components, Marcel Dekker, New York 1992 Zbl0755.62055MR1192783
- El-Bassiouni M. Y., Short confidence intervals for variance components, Comm. Statist. Theory Methods 23 (1994), 7, 1951–1933 (1994) Zbl0825.62194MR1281896
- 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
- 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
- Seely J., El-Bassiouni Y., Applying Wald’s variance component test, Ann. Statist. 11 (1983), 1, 197–201 (1983) Zbl0516.62028MR0684876
- 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
- 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
- Tukey J. W., Components in regression, Biometrics 7 (1951), 1, 33–69 (1951)
- Wald A., A note on the analysis of variance with unequal class frequencies, Ann. Math. Statist. 11 (1940), 96–100 (1940) MR0001502
- Wald A., A note on regression analysis, Ann. Math. Statist. 18 (1947), 4, 586–589 (1947) Zbl0029.30703MR0023498
- Williams J. S., A confidence interval for variance components, Biometrika 49 (1962), 1/2, 278–281 (1962) Zbl0138.13101MR0144424

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.