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SHORT COMMUNICATIONS

Efficient Robbins–Monro procedure for multivariate binary data

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Pages 172-180 | Received 06 Jan 2018, Accepted 31 Jul 2018, Published online: 07 Aug 2018

References

  • Anbar, D. (1978). A stochastic Newton–Raphson method. Journal of Statistical Planning and Inference, 2, 153–163. doi: 10.1016/0378-3758(78)90004-6
  • Azzalini, A. (2014). The skew-normal and related families. Cambridge: Cambridge University Press.
  • Azzalini, A., & Capitanio, A. (1999). Statistical applications of the multivariate skew normal distribution. Journal of the Royal Statistical Society, Series B, 61, 579–602. doi: 10.1111/1467-9868.00194
  • Chaloner, K., & Larntz, K. (1989). Optimal Bayesian design applied to logistic regression experiments. Journal of Statistical Planning and Inference, 21, 191–208. doi: 10.1016/0378-3758(89)90004-9
  • Chaudhuri, P., & Mykland, P. A. (1993). Nonlinear experiments: Optimal design and inference based on likelihood. Journal of the American Statistical Association, 88, 538–546. doi: 10.1080/01621459.1993.10476305
  • Cheung, Y. K. (2010). Stochastic approximation and modern model-based designs for dose-finding clinical trials. Statistical Science, 25, 191–201. doi: 10.1214/10-STS334
  • Chung, K. L. (1954). On a stochastic approximation method. Annals of Mathematical Statistics, 25, 463–483. doi: 10.1214/aoms/1177728716
  • Dror, H. A., & Steinberg, D. M. (2006). Robust experimental design for multivariate generalized linear models. Technometrics, 48, 520–529. doi: 10.1198/004017006000000318
  • Dror, H. A., & Steinberg, D. M. (2008). Sequential experimental designs for generalized linear models. Journal of the American Statistical Association, 103, 288–298. doi: 10.1198/016214507000001346
  • Duflo, M. (1997). Random iterative models. Berlin: Springer-Verlag.
  • Hung, Y., & Joseph, V. R. (2014). Discussion of “Three-phase optimal design of sensitivity experiments” by Wu and Tian. Journal of Statistical Planning and Inference, 149, 16–19. doi: 10.1016/j.jspi.2013.12.011
  • Joseph, V. R. (2004). Efficient Robbins–Monro procedure for binary data. Biometrika, 91, 461–470. doi: 10.1093/biomet/91.2.461
  • Kotz, S., & Nadarajah, S. (2004). Multivariate t distributions and their applications. Cambridge: Cambridge University Press.
  • Lai, T. L., & Robbins, H. (1979). Adaptive design and stochastic approximation. Annals of Statistics, 7, 1196–1221. doi: 10.1214/aos/1176344840
  • Neyer, B. T. (1994). A D-optimality-based sensitivity test. Technometrics, 36, 61–70. doi: 10.2307/1269199
  • Robbins, H., & Monro, S. (1951). A stochastic approximation method. Annals of Mathematical Statistics, 22, 400–407. doi: 10.1214/aoms/1177729586
  • Ruppert, D. (1985). A Newton-Raphson version of the multivariate Robbins-Monro procedure. Annals of Statistics, 13, 236–245. doi: 10.1214/aos/1176346589
  • Ruppert, D. (1988). Efficient estimators from a slowly convergent Robbins–Monro process. School of Operations Research and Industrial Engineering Technical Report, 781. Cornell University, Ithaca, NY.
  • Sacks, J. (1958). Asymptotic distribution of stochastic approximation procedures. Annals of Mathematical Statistics, 29, 373–405. doi: 10.1214/aoms/1177706619
  • Wei, C. Z. (1987). Multivariate adaptive stochastic approximation. Annals of Statistics, 15, 1115–1130. doi: 10.1214/aos/1176350496
  • Wetherill, G. B. (1963). Sequential estimation of quantal response curves. Journal of the Royal Statistical Society, Series B, 25, 1–48.
  • Wu, C. F. J. (1985). Efficient sequential designs with binary data. Journal of the American Statistical Association, 80, 974–984. doi: 10.1080/01621459.1985.10478213
  • Wu, C. F. J. (1986). Maximum likelihood recursion and stochastic approximation in sequential designs. In J. V. Ryzin (Ed.), IMS monograph series: Vol. 8. Adaptive statistical procedures and related topics (pp. 298–314). Hayward, CA: Institute of Mathematical Statistics.
  • Wu, C. F. J., & Tian, Y. (2014). Three-phase optimal design of sensitivity experiments. Journal of Statistical Planning and Inference, 149, 1–15. doi: 10.1016/j.jspi.2013.10.007
  • Young, L. J., & Easterling, R. G. (1994). Estimation of extreme quantiles based on sensitivity tests: A comparative study. Technometrics, 36, 48–60. doi: 10.1080/00401706.1994.10485400

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