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

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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

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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

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  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

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