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随机化最优设计的极小极大性AI 解读

A strategy of randomizing a design that is $L$-optimal for an ideal model is shown to possess a minimax property under a larger, more realistic model. This generalizes a result of Li.

实验随机化与正态理论推断的有效性AI 解读

This article examines how randomization helps to validate model-based probability statements. The asymptotic validity of normal-theory tests for means in multivariate linear models is established under general conditions. Numerical results are presented showing how randomization provides a limited degree of robustness in small experiments. The conditional relevance of randomization is also discussed. Consider the following additive model for a comparative experiment: Y = θ +…

实验随机化与正态理论推断的有效性AI 解读

This article examines how randomization helps to validate model-based probability statements. The asymptotic validity of normal-theory tests for means in multivariate linear models is established under general conditions. Numerical results are presented showing how randomization provides a limited degree of robustness in small experiments. The conditional relevance of randomization is also discussed. Consider the following additive model for a comparative experiment: Y = θ +…

Simultaneous confidence regions and simultaneous prediction regions are considered using the expected coverage measure criterion of Naiman. Invariance methods are used to construct minimax procedures in multivariate linear models.

不变置信区域与预测区域的一个条件性质AI 解读

This paper considers estimation and prediction problems invariant under an amenable group that is transitive on the parameter space. It is shown that an invariant confidence or prediction region does not admit super-relevant betting procedures if and only if its level of coverage is defined conditionally given the maximal invariant statistic.

一般多元方差分析模型中的同时区间估计AI 解读

Let $M \in M(m, p)$ be the matrix of means of interest in the GMANOVA problem. Our main results characterize all confidence sets for $M$ in a given class (invariant plus a weak additional restriction) that are exact for the families of parametric functions $a'Mb$ for all $a \in \mathbb{R}^m, b \in \mathbb{R}^p$ and $\operatorname{tr} N'M$ for all $N \in M(m, p)$. The corresponding families of smallest exact simultaneous confidence intervals are also given. Similar results…

具有最小期望测度的不变置信集AI 解读

A method is given for constructing a confidence set having smallest expected measure within the class of invariant level $1 - \alpha$ confidence sets. The main assumptions are (i) that the invariance group acts transitively on the parameter space and also acts on the parametric function of interest, and (ii) that the measure satisfies a certain equivariance property. When the invariance group satisfies the conditions of the Hunt-Stein Theorem, the optimal invariant…

置信集合估计中的充分性与不变性AI 解读

This paper describes how sufficiency and invariance considerations can be applied in problems of confidence set estimation to reduce the class of set estimators under investigation. Let $X$ be a random variable taking values in $\mathscr{X}$ with distribution $P_\theta, \theta \in \Theta$, and suppose a confidence set is desired for $\gamma = \gamma(\theta)$, where $\gamma$ takes values in $\Gamma$. The main tools used are (i) the representation of randomized set estimators…