Optimal Bayesian designs for models with partially specified heteroscedastic structure

• 成果类型: Article
• 署名作者: Dette, H; Wong, WK
• 署名单位: University of California System; University of California Los Angeles
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1996
• 页码: 2108-2127
• 关键词: exponential-growth model; robust experiment design

摘要

We consider the problem of finding a nonsequential optimal design for estimating parameters in a generalized exponential growth model. This problem is solved by first considering polynomial regression models with error variances that depend on the covariate value and unknown parameters. A Bayesian approach is adopted, and optimal Bayesian designs supported on a minimal number of support points for estimating the coefficients in the polynomial model are found analytically. For some criteria, the optimal Bayesian designs depend only on the expectation of the prior, but generally their dependence includes the derivative of the logarithm of the Laplace transform of a measure induced by the prior. The optimal design for the generalized exponential growth model is then determined from these optimal Bayesian designs.