Bootstrap methods for the up and down test on pyrotechnics sensitivity analysis

Statistica Sinica

Volumn 11, Issue 1, 2001, Pages 1-21

  Chao, M T ^a   Fuh, C D ^a  

^a INSTITUTE OF STATISTICAL SCIENCE   (Taiwan)

Author keywords

Bootstrap; Importance resampling; Markov chains; Maximum likelihood estimate; Probit model; Sequential design; Up and down method

Indexed keywords

EID: 0035608055     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (31)

1. Anderson, T. W. and Goodman, L. A. (1957). Statistical inference about Markov chains. Ann. Math. Statist. 28, 89-110.
2. Asmussen, S. and Rubinstein, R. Y. (1995). Steady state rare events simulation in queueing models and its complexity properties. In Frontiers in Queueing (Edited by J. Dhashalow). CRC Press, Boca Raton, Florida.
3. Athreya, K. B. and Fuh, C. D. (1992). Bootstrapping Markov chains: countable case. J. Statist. Plann. Inference 33, 311-331.
4. Basawa, I. V. and Prakasa Rao, B. L. S. (1980). Statistical Inference for Stochastic Processes. Academic Press, Inc., London.
5. Billingsley, P. (1961). Statistical Inference for Markov Processes. The University of Chicago Press, Chicago.
6. Bucklew, J. A., Ney, P. and Sadowsky, J. (1990). Monte Carlo simulation and large deviations theory for uniformly recurrent Markov chains. J. Appl. Probab. 27, 44-59.
7. Chao, M. T. and Fuh, C. D. (1997). Statistical analysis of the Bruceton test. Technical Report.
8. Chao, M. T. and Fuh, C. D. (1999). On Bruceton test for pyrotechnics sensitivity analysis. Proceedings of the 17th Symposium on Explosives and Pyrotechnic. 17 E&PS 5.1-5.29.
9. Datta, S. and McCormick, W. P. (1993). On the first order Edgeworth expansion for a Markov chain. J. Multivariate Anal. 44, 345-359.
10. Davison, A. C. and Hinkley, D. V. (1997). Bootstrap Methods and Their Application. Cambridge University Press, Cambridge.
11. Derman, C. (1957). Non-parametric up and down experimentation. Ann. Math. Statist. 30, 601-605.
12. Dixon, W. J. and Mood, A. M. (1948). A method for obtaining and analyzing sensitivity data. J. Amer. Statist. Assoc. 43, 109-126.
13. Do, K. A. and Hall, P. (1991). On importance resampling for the bootstrap. Biometrika 78, 161-167.
14. Efron, B. (1979). Bootstrap methods: another look at the jackknife. Ann. Statist. 7, 1-26.
15. Efron, B. and Tibshirani, R. (1993). An Introduction to the Bootstrap. Chapman & Hall, London.
16. Fuh, C. D. (1993). Statistical inquiry for Markov chains by bootstrap method. Statist. Sinica 3, 53-66.
17. Fuh, C. D. and Lai, T. L. (1998). Characteristic functions and Edgeworth expansions for Markov random walks with applications to bootstrap. Technical Report
18. Glynn, P. W. and Iglehart, D. L. (1989). Importance sampling for stochastic simulations. Management Sci. 35, 1367-1391.
19. Hampton, L. D., Blum, G. D. and Ayres, J. N. (1973). Logistic Anal. Bruceton Data. NOLTR, 73-91.
20. Johns, M. V. Jr. (1988). Importance sampling for bootstrap confidence intervals. J. Amer. Statist. Assoc. 83, 709-714.
21. Kulperger, R. J. and Prakasa Rao, B. L. S. (1990). Bootstrapping a finite state Markov chains. Sankhyā A 51, 178-191.
22. McMains, F. L. (1984). A digital computer program for a Bruceton analysis. Technical Memorandum 1254, U.S. Department of Commerce, Springfield, VA.
23. Mood, A. (1998). Personal communication.
24. Sitter, R. R. and Wu, C. F. J. (1993). Optimal designs for binary response experiments: Fieller, D, and A criteria. Scand. J. Statist. 20, 329-341.
25. Smith, W. D., Dutton, R. C. and Smith, N. TY (1996). A measure of association for assessing prediction accuracy that is a generalization of non-parametric ROC area. Statist. Medicine 15, 1199-1215.
26. Storer, B. E. (1989). Design and analysis of Phase I clinical trials. Biometrics 45, 925-937.
27. Thomas, E. V. (1994). Evaluating the ignition sensitivity of thermal-battery heat pellets. Technometrics 36, 273-282.
28. Wetherill, G. B. (1963). Sequential estimation of quantal response curves (with discussion). J. Roy. Statist. Soc. Ser. B 25, 1-48.
29. Wetherill, G. B. and Glazebrook, K. D. (1986). Sequential Methods in Statistics. Chapman and Hall, London.
30. Whitehead, J. and Brunier, H. (1995). Bayesian decision procedures for dose determining experiments. Statist. Medicine 14, 885-893.
31. Wu, C. F. J. (1985). Efficient sequential designs with binary data. J. Amer. Statist. Assoc. 80, 974-984.