FixedWidth Confidence Interval of P(X < Y) under a Data Dependent Adaptive Allocation Design
DOI:
https://doi.org/10.17713/ajs.v36i3.330Abstract
The present article is related to a nonparametric fixed-width confidence interval estimation of the parameter µ = P(X < Y ) = R F(y)dG(y), where F and G are two unknown continuous distribution functions. The estimation procedure is based on a sample obtained under some non-iid adaptive situation. We provide various asymptotic results related to the proposed procedure and compare it with a non-adaptive procedure.References
Anderson, T. W. (1960). A modification of the sequential probability ratio test to reduce the sample size. Annals of Mathematical Statistics, 31, 163-197.
Bandyopadhyay, U., and Biswas, A. (2004). An adaptive allocation for continuous response using Wilcoxon-Mann-Whitney score. Journal of Statistical Planning and Inference, 123, 207-224.
Bartlett, H. R., Roloff, D. W., Cornell, R. G., Andrew, A. F., Dillon, P. W., and Zwischesberger, J. B. (1985). Extracorporeal circulation in neonatal respiratory failure: A prospective randomized trial. Pediatrics, 76, 479-487.
Billingsley, P. (1968). Convergence of Probability Measures. New York: John Wiley.
Biswas, A., and Dewanji, A. (2004). Sequential adaptive designs for clinical trials with longitudinal response. In N. Mukhopadhyay, S. Chattopadhyay, and S. Datta (Eds.), Applied Sequential Methodologies. New York: Marcel Dekker.
Durham, S. D., Flournoy, N., and Li, W. (1998). A sequential design for maximizing the probability of a favourable response. Canadian Journal of Statistics, 26, 479-495.
Efron, B. (1971). Forcing a sequential experiment to be balanced. Biometrika, 58, 403-417.
Ghosh, M., Mukhopadhyay, N., and Sen, P. K. (1997). Sequential Estimation. New York: John Wiely.
Hall, P., and Heyde, C. C. (1980). Martingale Limit Theory and its Application. New York: Academic Press.
Hjort, N. L., and Fenstad, G. (1990). On the last n where |θ_n-θ| ≥ ε (Tech. Rep.). University of Oslo, Norway: Institute of Mathematics.
Hjort, N. L., and Fenstad, G. (1992). On the last n and the number of times an estimator is more than ε from its largest value. Annals of Statistics, 20, 469-489.
Hu, F., and Zhang, L. X. (2004). Asymptotic properties of doubly adaptive biased coin design for multi-treatment clinical trials. Annals of Statistics, 32, 268-301.
Laha, R. G., and Rohatgi, V. K. (1979). Probability Theory. New York: John Wiley.
Melfi, V., and Page, C. (2000). Estimation after adaptive allocation. Journal of Statistical Planning and Inference, 87, 353-363.
Melfi, V., Page, C., and Geraldes, M. (2001). An adaptive randomized design with application to estimation. Canadian Journal of Statistics, 29, 107-116.
Muller, H. H., and Schafer, H. (2001). Adaptive group sequential designs for clinical trials combining the advantages of adaptive and of classical group sequential approaches. Biometrics, 57, 886-891.
Rosenberger, W. F. (1993). Asymptotic inference with response-adaptive treatment allocation design. Annals of Statistics, 21, 2098-2107.
Rosenberger, W. F. (2002). Randomised urn models and sequential design. Sequential Analysis, 21, 1-28.
Rosenberger, W. F., and Sriram, T. N. (1997). Estimation for an adaptive allocation design. Journal of Statistical Planning and Inference, 59, 309-319.
Rosenberger, W. F., Stallard, N., Ivanova, A. V., Harper, C. N., and Ricks, M. L. (2001). Optimal adaptive designs for binary response trials. Biometrics, 57, 909-913.
Rout, C. C., Rocke, D. A., Levin, J., Gouws, E., and Reddy, D. (1993). A reevaluation of the role of crystalloid preload in the prevention of hypotension associated with spinal anesthesia for elective cesarean section. Anesthesiology, 79, 262-269.
Sen, P. K. (1981). Sequential Nonparametrics: Invariance Principles and Statistical Inference. New York: John Wiley.
Tamura, R. N., Faries, D. E., Andersen, J. S., and Heiligenstein, J. H. (1994). A case study of an adaptive clinical trials in the treatment of out-patients with depressive disorder. Journal of the American Statistical Association, 89, 768-776.
Ware, J. H. (1989). Investigating therapies of potentially great benefit: ECMO. Statistical Science, 4, 298-340.
Wei, L. J. (1979). The generalised Polya’s urn for sequential medical trials. Annals of Statistics, 7, 291-296.
Wei, L. J., and Durham, S. (1978). The randomized play-the-winner rule in medical trials. Journal of the American Statistical Association, 73, 838-843.
Wei, L. J., Smythe, R. T., Lin, D. Y., and Park, T. S. (1990). Statistical inference with data-dependent treatment allocation rules. Journal of the American Statistical Association, 85, 156-162.
Zelen, M. (1969). Play-the-winner rule and the controlled clinical trial. Journal of the American Statistical Association, 64, 131-146.
Downloads
Published
Issue
Section
License
The Austrian Journal of Statistics publish open access articles under the terms of the Creative Commons Attribution (CC BY) License.
The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed.
Copyright on any research article published by the Austrian Journal of Statistics is retained by the author(s). Authors grant the Austrian Journal of Statistics a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified.
Manuscripts should be unpublished and not be under consideration for publication elsewhere. By submitting an article, the author(s) certify that the article is their original work, that they have the right to submit the article for publication, and that they can grant the above license.
How to Cite
