Small-sample corrections for score tests in Birnbaum-Saunders regressions. (English) Zbl 1208.62154
Summary: We deal with the issue of performing accurate small-sample inference in the Z. W. Birnbaum and S. C. Saunders [J. Appl. Probab. 6, 319–327 (1969; Zbl 0209.49801)] regression model, which can be useful for modeling life time or reliability data. We derive a Bartlett-type correction for the score test and compare numerically the corrected test with the usual score test and some other competitors.
MSC:
| 62N03 | Testing in survival analysis and censored data |
| 65C05 | Monte Carlo methods |
| 62G10 | Nonparametric hypothesis testing |
Keywords:
Bartlett-type correction; chi-square distribution; fatigue life distribution; life time data; likelihood ratio test; reliability dataCitations:
Zbl 0209.49801References:
| [1] | Abell M. L., Statistics with Maple (2002) |
| [2] | Abramowitz M., Handbook of Mathematical Functions (1970) |
| [3] | DOI: 10.2307/3212003 · Zbl 0209.49801 · doi:10.2307/3212003 |
| [4] | DOI: 10.1111/1467-9574.00237 · Zbl 1090.62546 · doi:10.1111/1467-9574.00237 |
| [5] | Cordeiro G. M., Biometrika 78 pp 573– (1991) |
| [6] | DOI: 10.1080/00949659808811928 · Zbl 1126.62341 · doi:10.1080/00949659808811928 |
| [7] | DOI: 10.1080/07474939608800361 · Zbl 0885.62021 · doi:10.1080/07474939608800361 |
| [8] | DOI: 10.1093/biomet/82.2.426 · Zbl 0824.62061 · doi:10.1093/biomet/82.2.426 |
| [9] | DOI: 10.2307/3315148 · Zbl 0581.60073 · doi:10.2307/3315148 |
| [10] | DOI: 10.1016/j.jspi.2003.11.007 · Zbl 1087.62011 · doi:10.1016/j.jspi.2003.11.007 |
| [11] | Doornik J. A., Ox: An Object-Oriented Matrix Language., 5. ed. (2006) |
| [12] | DOI: 10.1080/00949659708811854 · Zbl 0886.62022 · doi:10.1080/00949659708811854 |
| [13] | DOI: 10.1080/0266476042000280409 · Zbl 1121.62370 · doi:10.1080/0266476042000280409 |
| [14] | DOI: 10.1016/j.spl.2008.08.014 · Zbl 1155.62006 · doi:10.1016/j.spl.2008.08.014 |
| [15] | Gradshteyn I. S., Table of Integrals, Series, and Products (2007) · Zbl 1208.65001 |
| [16] | DOI: 10.1093/biomet/72.3.653 · Zbl 0586.62034 · doi:10.1093/biomet/72.3.653 |
| [17] | DOI: 10.1093/biomet/83.4.923 · Zbl 0883.62023 · doi:10.1093/biomet/83.4.923 |
| [18] | DOI: 10.1016/j.csda.2007.09.021 · Zbl 1452.62729 · doi:10.1016/j.csda.2007.09.021 |
| [19] | DOI: 10.1016/j.csda.2006.09.020 · Zbl 1445.62199 · doi:10.1016/j.csda.2006.09.020 |
| [20] | DOI: 10.1016/j.csda.2006.08.016 · Zbl 1162.62419 · doi:10.1016/j.csda.2006.08.016 |
| [21] | DOI: 10.1016/j.csda.2009.11.017 · Zbl 1464.62118 · doi:10.1016/j.csda.2009.11.017 |
| [22] | R Development Core Team ( 2008 ).R: A Language and Environment for Statistical Computing.R Foundation for Statistical Computing, Vienna, Austria . |
| [23] | Rieck , J. R. ( 1989 ). Statistical analysis for the Birnbaum–Saunders fatigue life distribution. Ph.D. thesis, Department of Mathematical Sciences, Clemson University, Clemson, SC . |
| [24] | DOI: 10.1080/03610929508831581 · Zbl 0937.62564 · doi:10.1080/03610929508831581 |
| [25] | DOI: 10.1080/03610929908832416 · Zbl 0935.62020 · doi:10.1080/03610929908832416 |
| [26] | DOI: 10.2307/1269007 · Zbl 0717.62090 · doi:10.2307/1269007 |
| [27] | DOI: 10.1080/03610920701541174 · Zbl 1136.62016 · doi:10.1080/03610920701541174 |
| [28] | DOI: 10.1081/STA-100001567 · Zbl 1008.62562 · doi:10.1081/STA-100001567 |
| [29] | DOI: 10.1016/j.csda.2006.08.030 · Zbl 1163.62057 · doi:10.1016/j.csda.2006.08.030 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
