AN EFFICIENT SEQUENTIAL DESIGN FOR SENSITIVITY EXPERIMENTS

• Published in: Acta mathematica scientia Vol. 30; no. 1; pp. 269 - 280
• Main Author: 田玉斌 房永飞
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 2010; Department of Mathematics, School of Science, Beijing Institute of Technology, Beijing 100081, China
• Subjects: 62F25; 62L05; Approximation; Bayesian strategy; bootstrap principle; Consistency; Estimators; extreme quantiles; Historic; Mathematical analysis; Mathematical models; Quantiles; sensitivity experiments; sequential design; Strategy; 二进制; 合理分配; 序列设计; 敏感性试验; 试点单位; 贝叶斯策略; 高阶近似; 62L05; extreme quantiles; bootstrap principle; Bayesian strategy; sequential design; sensitivity experiments; 62F25
• ISSN: 0252-9602; 1572-9087
• DOI: 10.1016/S0252-9602(10)60044-6

In sensitivity experiments, the response is binary and each experimental unit has a critical stimulus level that cannot be observed directly. It is often of interest to estimate extreme quantiles of the distribution of these critical stimulus levels over the tested products. For this purpose a new sequential scheme is proposed with some commonly used models. By using the bootstrap repeated-sampling principle, reasonable prior distributions based on a historic data set are specified. Then, a Bayesian strategy for the sequential procedure is provided and the estimator is given. Further, a high order approximation for such an estimator is explored and its consistency is proven. A simulation study shows that the proposed method gives superior performances over the existing methods.