Asymptotic Inference from Sequential Design in a Nonlinear Situation.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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This document shows that confidence regions constructed by the repeated-sampling principle are asymptotically valid for sequential designs in general linear models and nonlinear parameters. For estimation of parameters in nonlinear models or nonlinear parameters in linear models, sequential design of experiment is often used to best utilize the information. It results in saving the number of runs. After the termination of the experiment with a fixed sample size, inference such as hypothesis testing or confidence interval about the parameter is made. The classical repeated-sampling principle of inference can not be applied because it relies on the repetition of the same design while in the sequential setting it is not repeatable. By using the martingale as a technical tool, it is shown that, at least for large samples, such inference is still justified. The companion questions of consistency of parameter estimators and convergence of sequential design to an optimal design are also answered. Keywords Statistics Probability.
- Statistics and Probability