Efficient sequential designs with binary data

Journal of the American Statistical Association

Volumn 80, Issue 392, 1985, Pages 974-984

  Wu, C F Jeff ^a  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

Logit; Optimal design; Quantal response curve; Robbins Monro stochastic approximation; Sensitivity experiments; Spearman K rber estimator; Up and down method

Indexed keywords

EID: 84950861150     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1985.10478213     Document Type: Article

References (31)

1. Abdelhamid, S. N. (1973), “Transformations of Observations in Stochastic Approximation,” Annals of Statistics, 1, 1158–1174.
2. Anbar, D. (1973), “On Optimal Estimation Methods Using Stochastic Approximation Procedures,” Annals of Statistics, 1, 1175–1184.
3. —— (1978), “A Stochastic Newton-Raphson Method,” Journal of Statistical Planning and Inference, 2, 153–163.
4. 2Estimates of the Logistic Function,” Journal of the American Statistical Association, 50, 130–162.
5. Chambers, E. A., and Cox, D. R. (1967), “Discrimination Between Alternative Binary Response Models,” Biometrika, 54, 573–578.
6. Chung, K. L. (1954), “On a Stochastic Approximation Method,” Annals of Mathematical Statistics, 25, 463–483.
7. Cochran, W. G., and Davis, M. (1965), “The Robbins–Monro Method for Estimating the Median Lethal Dose, “Journal of the Royal Statistical Society, Ser. B, 27, 28–44.
8. Cox, D. R. (1970), Analysis of Binary Data, London: Methuen.
9. Davis, M. (1971), “Comparison of Sequential Bioassays in Small Samples,” Journal of the Royal Statistical Society, Ser. B, 33, 78–87.
10. Dixon, W. J., and Mood, A. M. (1948), “A Method for Obtaining and Analyzing Sensitivity Data,” Journal of the American Statistical Association, 43, 109–126.
11. Dubins, L. E., and Freedman, D. A. (1965), “A Sharper Form of the Borel–Cantelli Lemma and the Strong Law,” Annals of Mathematical Statistics, 36, 800–807.
12. Fabian, V. (1973), “Asymptotically Efficient Stochastic Approximation: The RM Case,” Annals of Statistics, 1, 486–495.
13. —— (1983), “A Locally Asymptotic Minimax Optimality of an Adaptive Robbins-Monro Stochastic Approximation Procedure,” in Mathematical Learning Models—Theory and Algorithms, eds. U. Herkenrath, D. Kalin, and W. Vogel, New York: Springer-Verlag, pp. 43–49.
14. Finney, D. J. (1978), Statistical Method in Biological Assay, London: Griffin.
15. Freeman, P. R. (1970), “Optimal Bayesian Sequential Estimation of the Median Effective Dose,” Biometrika, 57, 79–89.
16. Hodges, J. L., and Lehmann, E. L. (1955), “Two Approximations to the Robbins-Monro Process,” Proceedings of the 3rd Berkeley Symposium, 1, 95–104.
17. Lai, T. L., and Robbins, H. (1979), “Adaptive Design and Stochastic Approximation,” Annals of Statistics, 7, 1196–1221.
18. —— (1981), “Consistency and Asymptotic Efficiency of Slope Estimates in Stochastic Approximation Schemes,” Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 56, 329–360.
19. Leonard, T. (1982), “An Inferential Approach to the Bioassay Design Problem,” Technical Summary Report 2416, University of Wisconsin-Madison, Mathematics Research Center.
20. Lord, F. M. (1971), “Tailored Testing, An Application of Stochastic Approximation,” Journal of the American Statistical Association, 66, 707–711.
21. Miller, R. G., and Halpern, J. W. (1980), “Robust Estimators for Quantal Bioassay,” Biometrika, 67, 103–110.
22. Owen, R. J. (1975), “A Bayesian Sequential Procedure for Quantal Response in the Context of Adaptive Mental Testing,” Journal of the American Statistical Association, 70, 351–356.
23. Robbins, H., and Monro, S. (1951), “A Stochastic Approximation Method,” Annals of Mathematical Statistics, 29, 400–407.
24. Robbins, H., and Siegmund, D. (1971), “A Convergence Theorem for Nonnegative Almost Sure Supermartingale and Some Applications, “in Optimization Methods in Statistics, ed. J. N. Rustagi, New York: Academic Press, pp. 233–257.
25. Rose, R. M., Teller, D. Y., and Rendleman, P. (1970), “Statistical Properties of Staircase Estimates,” Perception and Psychophysics, 8, 199–204.
26. Sacks, J. (1958), “Asymptotic Distribution of Stochastic Approximation Procedures,” Annals of Mathematical Statistics, 29, 373–405.
27. Silvapulle, M. J. (1981), “On the Existence ofMaximum Likelihood Estimators for the Binomial Response Model,” Journal of the Royal Statistical Society, Ser. B, 43, 310–313.
28. Tsutakawa, R. K. (1972), “Design of Experiment for Bioassay,” Journal of the American Statistical Association, 67, 584–590.
29. Wetherill, G. B. (1963), “Sequential Estimation of Quantal Response Curves” (with discussion), Journal of the Royal Statistical Society, Ser. B, 25, 1–48.
30. —— (1966), Sequential Methods in Statistics, London: Methuen.
31. Wu, C. F. J. (1983), “Efficient Model-Based Sequential Designs for Sensitivity Experiments,” Technical Summary Report 2563, University of Wisconsin–Madison, Mathematics Research Center.