Two-sided Tolerance Intervals in a Simple Linear Regression
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2013)
- Volume: 52, Issue: 2, page 31-41
- ISSN: 0231-9721
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topChvosteková, Martina. "Two-sided Tolerance Intervals in a Simple Linear Regression." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 52.2 (2013): 31-41. <http://eudml.org/doc/260835>.
@article{Chvosteková2013,
abstract = {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.},
author = {Chvosteková, Martina},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {multiple-use confidence interval; simultaneous two-sided tolerance interval; multiple-use confidence interval; simultaneous two-sided tolerance interval},
language = {eng},
number = {2},
pages = {31-41},
publisher = {Palacký University Olomouc},
title = {Two-sided Tolerance Intervals in a Simple Linear Regression},
url = {http://eudml.org/doc/260835},
volume = {52},
year = {2013},
}
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
PB - Palacký University Olomouc
VL - 52
IS - 2
SP - 31
EP - 41
AB - 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.
LA - eng
KW - multiple-use confidence interval; simultaneous two-sided tolerance interval; multiple-use confidence interval; simultaneous two-sided tolerance interval
UR - http://eudml.org/doc/260835
ER -
References
top- Chvosteková, M., 10.1080/03610926.2012.724502, Communications in Statistics, Theory and Methods 42 (2013), 1145–1152. (2013) MR3031273DOI10.1080/03610926.2012.724502
- Chvosteková, M., Determination of two-sided tolerance interval in a linear regression model, Forum Statisticum Slovacum 6 (2010), 79–84. (2010)
- Chvosteková, M., Witkovský, V., 10.2478/v10048-009-0003-9, Measurement Science Review 9 (2009), 1–8. (2009) DOI10.2478/v10048-009-0003-9
- Krishnamoorthy, K., Mathew, T., Statistical Tolerance Regions: Theory, Applications, and Computation, Wiley series in probability and statistics, Wiley, Chichester, 2009. (2009) MR2500599
- Lee, Y., Mathew, T., Advances on Theoretical and Methodological Aspects of Probability and Statistics, Taylor & Francis, London, 2002. (2002) MR1987243
- Lieberman, G. J., Miller, R. G., Jr., 10.1093/biomet/50.1-2.155, Biometrika 50 (1963), 155–168. (1963) Zbl0124.35501MR0158472DOI10.1093/biomet/50.1-2.155
- Lieberman, G. J., Miller, R. G., Hamilton, M. A., 10.1093/biomet/54.1-2.133, Biometrika 54 (1967), 133–145. (1967) MR0217953DOI10.1093/biomet/54.1-2.133
- Limam, M. M. T., Thomas, R., 10.1080/01621459.1988.10478666, Journal of the American Statistical Association 83 (1988), 801–804. (1988) Zbl0649.62030MR0963808DOI10.1080/01621459.1988.10478666
- Mee, R. W., Eberhardt, K. R., 10.1080/00401706.1996.10484501, Technometrics 38 (1996), 221–229. (1996) MR1411879DOI10.1080/00401706.1996.10484501
- Mee, R. W., Eberhardt, K. R., Reeve, C. P., 10.1080/00401706.1991.10484808, Technometrics 33 (1991), 211–219. (1991) MR1110358DOI10.1080/00401706.1991.10484808
- Scheffé, H., 10.1214/aos/1193342379, The Annals of Statistics 1 (1973), 1–37. (1973) MR0336920DOI10.1214/aos/1193342379
- Wilson, A. L.:, 10.1214/aoms/1177698707, The Annals of Mathematical Statistics 38 (1967), 1536–1540. (1967) Zbl0183.20902MR0217954DOI10.1214/aoms/1177698707
- Witkovský, V.:, On exact multiple-use linear calibration confidence intervals, In: MEASUREMENT 2013: 9th International Conference on Measurement, Smolenice, Slovakia, 2013, 35–38. (2013)
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