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 o...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.展开更多
Maximum likelihood recursions were used by Wu （1985） to estimate extreme quantiles of a quantal response curve. For certain choices of initial designs, Wu＇s method performs well. In many fields of application, ther...Maximum likelihood recursions were used by Wu （1985） to estimate extreme quantiles of a quantal response curve. For certain choices of initial designs, Wu＇s method performs well. In many fields of application, there often exist some different initial designs which are known as the up-and- down designs. Based on the existing data set from such a design, the authors propose three sequential empirical Bayesian designs by quickly and efficiently exploiting the information in the testing data and known knowledge. The improvement obtained by using the new procedures for the estimation of extreme quantiles is substantial.展开更多
文摘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.
基金This research is supported by the National Natural Science Foundation of China under Grant No. 10971012.
文摘Maximum likelihood recursions were used by Wu （1985） to estimate extreme quantiles of a quantal response curve. For certain choices of initial designs, Wu＇s method performs well. In many fields of application, there often exist some different initial designs which are known as the up-and- down designs. Based on the existing data set from such a design, the authors propose three sequential empirical Bayesian designs by quickly and efficiently exploiting the information in the testing data and known knowledge. The improvement obtained by using the new procedures for the estimation of extreme quantiles is substantial.
