Prediction intervals for general balanced linear random models

Journal of Statistical Planning and Inference

Volumn 138, Issue 10, 2008, Pages 3164-3175

  Lin, T Y ^a   Liao, C T ^b  

^a FENG CHIA UNIVERSITY   (Taiwan)

^b NATIONAL TAIWAN UNIVERSITY   (Taiwan)

Author keywords

Generalized confidence interval; Generalized p value; Variance component

Indexed keywords

EID: 45049086777     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2008.01.001     Document Type: Article

References (30)

1. Burch B.D. Generalized confidence intervals for proportions of total variance in mixed linear models. J. Statist. Plann. Inference 137 (2007) 2394-2404
2. Chew V. Simultaneous prediction intervals. Technometrics 10 (1968) 323-330
3. Chou Y.M., and Owen D.B. One-sided simultaneous lower prediction intervals for l future samples from a normal distribution. Technometrics 28 (1986) 247-251
4. Davis C.B., and McNichols R.J. One-sided intervals for at least p of m observations from a normal population on each of r future occasions. Technometrics 29 (1987) 359-370
5. Efron B., and Tibshirani R.J. An Introduction to the Bootstrap (1993), Chapman & Hall, New York
6. Fertig K.W., and Mann N.R. One-sided prediction intervals for at least p out of m future observations for a normal population. Technometrics 9 (1977) 167-177
7. Genz A. Finding critical values using numerical integration. Comput. Sci. Statist. 31 (1999) 263-266
8. Genz A., and Bretz F. Comparison of methods for the computation of multivariate t probabilities. J. Comput. Graph. Statist. 11 (2002) 950-971
9. Graybill F.A. Theory and Application of the Linear Model (1976), Wadsworth, Belmont, CA
10. Hahn G.J. Factor for calculating two-sided prediction intervals for samples from a normal distribution. J. Amer. Statist. Assoc. 64 (1969) 878-888
11. Hahn G.J. Additional factors for calculating prediction intervals for samples from a normal distribution. J. Amer. Statist. Assoc. 65 (1970) 1668-1676
12. Hahn G.J., and Meeker W.Q. Statistical Intervals (1991), Wiley, New York
13. Hall I.J., and Prairie R.R. One-sided prediction intervals to contain at least m out of k future observations. Technometrics 15 (1973) 897-914
14. Hamada M., and Weerahandi S. Measurement system assessment via generalized inference. J. Qual. Technol. 32 (2000) 241-253
15. Hanning J., Iyer H.K., and Patterson P. Fiducial generalized confidence intervals. J. Amer. Statist. Assoc. 101 (2006) 254-269
16. Houf R.F., and Berman D.B. Statistical analysis of power module thermal test equipment performance. IEEE Trans. Components Hybrids Manufacturing Technol. 11 4 (1988) 516-520
17. Iyer H.K., Wang C.M., and Mathew T. Models and confidence intervals for true values in interlaboratory trials. J. Amer. Statist. Assoc. 99 (2004) 1060-1071
18. Khuri A.I., Mathew T., and Sinha B.K. Statistical Tests for Mixed Linear Models (1998), Wiley, New York
19. Liao C.T., and Iyer H.K. A tolerance interval for the normal distribution with several variance components. Statist. Sin. 14 (2004) 217-229
20. Liao C.T., Lin T.Y., and Iyer H.K. One- and two-sided tolerance intervals for general balanced mixed models and unbalanced one-way random models. Technometrics 47 (2005) 323-335
21. Lin S.H., Lee J.C., and Wang R.S. Generalized inferences on the common mean vector of several multivariate normal populations. J. Statist. Plann. Inference 137 (2007) 2240-2249
22. Lin T.Y., and Liao C.T. A β-expectation tolerance interval for general balanced mixed linear models. Comput. Statist. Data Anal. 50 (2006) 911-925
23. Mathew T., and Webb D.W. Generalized p-values and confidence intervals for variance components: applications to army test and evaluation. Technometrics 47 (2005) 312-322
24. Miller, Jr., R.G., 1981. Simultaneous Statistical Inference, second ed. Springer, New York.
25. Odeh R.E. Two-sided prediction intervals to contain at least k out of m future observations from a normal distribution. Technometrics 32 (1990) 203-216
26. Satterthwaite F.E. An approximate distribution of estimates of variance components. Biom. Bull. 2 (1946) 110-114
27. Tsui K.W., and Weerahandi S. Generalized p-values in significance testing of hypotheses in the presence of nuisance parameters. J. Amer. Statist. Assoc. 84 (1989) 602-607
28. Wang C.M. Prediction intervals for a balanced one-way random-effects model. Commun. Stat. Simul. Comput. 21 (1992) 671-687
29. Weerahandi S. Generalized confidence intervals. J. Amer. Statist. Assoc. 88 (1993) 899-905
30. Weerahandi S. Exact Statistical Methods for Data Analysis (1995), Springer, New York