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一维自回归误差过程下的最优与极小极大精确处理设计AI 解读

A theory is developed following work by Williams (1952) and Kiefer (1960) for exact treatment designs in one dimension in which the errors are a stationary process. It is shown that the designs which achieve the minimax value of any of a wide class of functionals on the information matrix for estimation of treatment differences have a special property. If the process is autoregressive of order $p$ then a random piece of the design of length $p + 1$ exhibits uncorrelated…

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条件置信陈述与置信度估计量AI 解读

Procedures are given for assessing the conclusiveness of a decision in terms of a (chance) conditional confidence coefficient Γ that has frequentist interpretability analogous to that of a traditional confidence coefficient. Properties of such procedures are compared in terms of the distribution of Γ. This leads to recommendations on the choice of conditioning. Also, a methodology for estimating the confidence when it depends on unknown parameter values is given. The notions…

高次数多项式回归的最优设计AI 解读

Polynomial regression of degree $n$ on an interval is considered. Optimal designs $\xi_n$ are discussed for various optimality criteria. The behavior of $\xi_n$ for large $n$ is investigated and comparisons of $\xi_n$ with the limiting design $\xi_0$ are made.

最优近似设计的一般等价理论AI 解读

For general optimality criteria $\Phi$, criteria equivalent to $\Phi$-optimality are obtained under various conditions on $\Phi$. Such equivalent criteria are useful for analytic or machine computation of $\Phi$-optimum designs. The theory includes that previously developed in the case of $D$-optimality (Kiefer-Wolfowitz) and $L$-optimality (Karlin-Studden-Fedorov), as well as $E$-optimality and criteria arising in response surface fitting and minimax extrapolation.…