Geodesic
Two-sided Tolerance Intervals in a Simple Linear Regression
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 52 (2013) no. 2, pp. 31-41 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Numerical results for a simple linear regression indicate that the non-simultaneous two-sided tolerance intervals nearly satisfy the condition of multiple-use confidence intervals, see Lee and Mathew (2002), but the numerical computation of the limits of the multiple-use confidence intervals is needed. We modified the Lieberman–Miller method (1963) for computing the simultaneous two-sided tolerance intervals in a simple linear regression with independent normally distributed errors. The suggested tolerance intervals are the narrowest of all the known simultaneous two-sided tolerance intervals. The computation of the multiple-use confidence intervals based on the new simultaneous two-sided tolerance intervals is simple and fast.
Numerical results for a simple linear regression indicate that the non-simultaneous two-sided tolerance intervals nearly satisfy the condition of multiple-use confidence intervals, see Lee and Mathew (2002), but the numerical computation of the limits of the multiple-use confidence intervals is needed. We modified the Lieberman–Miller method (1963) for computing the simultaneous two-sided tolerance intervals in a simple linear regression with independent normally distributed errors. The suggested tolerance intervals are the narrowest of all the known simultaneous two-sided tolerance intervals. The computation of the multiple-use confidence intervals based on the new simultaneous two-sided tolerance intervals is simple and fast.
Classification : 62F25, 62J05
Keywords: multiple-use confidence interval; simultaneous two-sided tolerance interval 
@article{AUPO_2013_52_2_a2,
     author = {Chvostekov\'a, Martina},
     title = {Two-sided {Tolerance} {Intervals} in a {Simple} {Linear} {Regression}},
     journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
     pages = {31--41},
     year = {2013},
     volume = {52},
     number = {2},
     mrnumber = {3202377},
     zbl = {06296012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUPO_2013_52_2_a2/}
}
TY  - JOUR
AU  - Chvosteková, Martina
TI  - Two-sided Tolerance Intervals in a Simple Linear Regression
JO  - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY  - 2013
SP  - 31
EP  - 41
VL  - 52
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/AUPO_2013_52_2_a2/
LA  - en
ID  - AUPO_2013_52_2_a2
ER  - 
%0 Journal Article
%A Chvosteková, Martina
%T Two-sided Tolerance Intervals in a Simple Linear Regression
%J Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
%D 2013
%P 31-41
%V 52
%N 2
%U http://geodesic.mathdoc.fr/item/AUPO_2013_52_2_a2/
%G en
%F AUPO_2013_52_2_a2
Chvosteková, Martina. Two-sided Tolerance Intervals in a Simple Linear Regression. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 52 (2013) no. 2, pp. 31-41. http://geodesic.mathdoc.fr/item/AUPO_2013_52_2_a2/

[1] Chvosteková, M.: Simultaneous two-sided tolerance intervals for a univariate linear regression model. Communications in Statistics, Theory and Methods 42 (2013), 1145–1152. | DOI | MR

[2] Chvosteková, M.: Determination of two-sided tolerance interval in a linear regression model. Forum Statisticum Slovacum 6 (2010), 79–84.

[3] Chvosteková, M., Witkovský, V.: Exact likelihood ratio test for the parameters of the linear regression model with normal errors. Measurement Science Review 9 (2009), 1–8. | DOI

[4] Krishnamoorthy, K., Mathew, T.: Statistical Tolerance Regions: Theory, Applications, and Computation. Wiley series in probability and statistics, Wiley, Chichester, 2009. | MR

[5] Lee, Y., Mathew, T.: Advances on Theoretical and Methodological Aspects of Probability and Statistics. Taylor & Francis, London, 2002. | MR

[6] Lieberman, G. J., Miller, R. G., Jr.: Simultaneous Tolerance intervals in regression. Biometrika 50 (1963), 155–168. | DOI | MR | Zbl

[7] Lieberman, G. J., Miller, R. G., Hamilton, M. A.: Unlimited simultaneous discrimination intervals in regression. Biometrika 54 (1967), 133–145. | DOI | MR

[8] Limam, M. M. T., Thomas, R.: Simultaneous tolerance intervals for the linear regression model. Journal of the American Statistical Association 83 (1988), 801–804. | DOI | MR | Zbl

[9] Mee, R. W., Eberhardt, K. R.: A Comparison of Uncertainty Criteria for Calibration. Technometrics 38 (1996), 221–229. | DOI | MR

[10] Mee, R. W., Eberhardt, K. R., Reeve, C. P.: Calibration and simultaneous tolerance intervals for regression. Technometrics 33 (1991), 211–219. | DOI | MR

[11] Scheffé, H.: A statistical theory of calibration. The Annals of Statistics 1 (1973), 1–37. | DOI | MR

[12] Wilson, A. L.:: An approach to simultaneous tolerance intervals in regression. The Annals of Mathematical Statistics 38 (1967), 1536–1540. | DOI | MR | Zbl

[13] Witkovský, V.:: On exact multiple-use linear calibration confidence intervals. In: MEASUREMENT 2013: 9th International Conference on Measurement, Smolenice, Slovakia, 2013, 35–38.