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变量测量误差模型的局部最优设计AI 解读

We consider the construction of optimal designs for nonlinear regression models when there are measurement errors in the covariates. Corresponding approximate design theory is developed for maximum likelihood and least-squares estimation, with the latter leading to nonconcave optimization problems. Analytical characterizations of the locally D-optimal saturated designs are provided for the Michaelis–Menten, |$E_{\rm max}$| and exponential regression models. Through concrete…

加性部分非线性模型的最优设计AI 解读

We develop optimal design theory for additive partially nonlinear regression models, and show that D-optimal designs can be found as the products of the corresponding D-optimal designs in one dimension. For partially nonlinear models, D-optimal designs depend on the unknown nonlinear model parameters, and misspecifications of these parameters can lead to poor designs. Hence we generalise our results to parameter robust optimality criteria, namely Bayesian and standardised…

emax、对数线性与指数模型的最优设计AI 解读

We derive locally D- and EDp-optimal designs for the exponential, log-linear and three-parameter emax models. For each model the locally D- and EDp-optimal designs are supported at the same set of points, while the corresponding weights are different. This indicates that for a given model, D-optimal designs are efficient for estimating the smallest dose that achieves 100p% of the maximum effect in the observed dose range. Conversely, EDp-optimal designs also yield good…

区分嵌套回归模型的序贯与非序贯设计比较AI 解读

SUMMARY Classical regression analysis is usually performed in two steps. In a first step an appro priate model is identified to describe the data-generating process and in a second step statistical inference is performed in the identified model. In this paper we investigate a sequential and a non-sequential design strategy, which take into account these different goals of the analysis for a class of nested models. It is demonstrated that non-sequential designs usually…

线性回归模型中的极小极大设计AI 解读

In the usual linear regression model we investigate the geometric structure of a class of minimax optimality criteria containing Elfving's minimax and Kiefer's $\phi_p$-criteria as special cases. It is shown that the optimal designs with respect to these criteria are also optimal for $A'\theta$, where $A$ is any inball vector (in an appropriate norm) of a generalized Elfving set. The results explain the particular role of the $A$- and $E$-optimality criterion and are applied…

多项式回归中 D 与 D₁ 最优设计的推广AI 解读

In the class of polynomial regression models up to degree $n$ we determine the design on $\lbrack -1, 1\rbrack$ that maximizes a product of $n + 1$ determinants of information matrices weighted with a prior $\beta$, where the $l$-th information matrix corresponds to a polynomial regression model of degree $l$, for $l = 0, 1, \cdots, n$. The designs are calculated using canonical moments. We identify a special class of priors $\beta(z)$ depending on one real parameter $z$ so…