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定性因子实验中高斯随机场的信号混杂AI 解读

Signal aliasing is an inevitable consequence of using fractional factorial designs. Unlike linear models with fixed factorial effects, for Gaussian random field models advocated in some Bayesian design and computer experiment literature, the issue of signal aliasing has not received comparable attention. In the present article, this issue is tackled for experiments with qualitative factors. The signals in a Gaussian random field can be characterized by the random effects…

利用循环偏置称重设计构造最优 fMRI 实验AI 解读

Functional magnetic resonance imaging (fMRI) technology is popularly used in many fields for studying how the brain reacts to mental stimuli. The identification of optimal fMRI experimental designs is crucial for rendering precise statistical inference on brain functions, but research on this topic is very lacking. We develop a general theory to guide the selection of fMRI designs for estimating a hemodynamic response function (HRF) that models the effect over time of the…

最小混杂的一般理论及其应用AI 解读

Minimum aberration is an increasingly popular criterion for comparing and assessing fractional factorial designs, and few would question its importance and usefulness nowadays. In the past decade or so, a great deal of work has been done on minimum aberration and its various extensions. This paper develops a general theory of minimum aberration based on a sound statistical principle. Our theory provides a unified framework for minimum aberration and further extends the…

具有最大估计容量的分块正规部分因子设计AI 解读

In this paper, the problem of constructing optimal blocked regular fractional factorial designs is considered. The concept of minimum aberration due to Fries and Hunter is a well­accepted criterion for selecting good unblocked fractional factorial designs. Cheng, Steinberg and Sun showed that a minimum aberration design of resolution three or higher maximizes the number of two­factor interactions which are not aliases of main effects and also tends to distribute these…

二水平分数因子设计的最优分区组理论AI 解读

In this paper, we define the blocking wordlength pattern of a blocked fractional factorial design by combining the wordlength patterns of treatment-defining words and block-defining words. The concept of minimum aberration can be defined in terms of the blocking wordlength pattern and provides a good measure of the estimation capacity of a blocked fractional factorial design. By blending techniques of coding theory and finite projective geometry, we obtain combinatorial…

置换不变设计区域上设计矩阵的完全类结果AI 解读

In 1987 Cheng determined $\phi_p$-optimal designs for linear regression (without intercept) over the $n$-dimensional unit cube $\lbrack 0, 1\rbrack^n$ for $-\infty \leq p \leq 1$. These are uniform distributions on the vertices with a fixed number of entries equal to unity, and mixtures of neighboring such designs. In 1989 Pukelsheim showed that this class of designs is essentially complete and that the corresponding class of moment matrices is minimally complete, with…

趋势稳健的两水平析因设计AI 解读

Limiting the possible influence of time order effects may be an important consideration in designing a sequential experiment. We consider the problem of finding trend robust run orders of two-level factorials when the time effects are modelled via a first order autoregressive error model or via a time series model. In both cases, run orders are trend robust if the factors change level many times. Other run orders can be quite inefficient, even if they are free of low-degree…

抗趋势的两水平析因试验设计AI 解读

Limiting the possible influence of time order effects may be an important consideration in designing a sequential experiment. We consider the problem of finding trend robust run orders of two-level factorials when the time effects are modelled via a first order autoregressive error model or via a time series model. In both cases, run orders are trend robust if the factors change level many times. Other run orders can be quite inefficient, even if they are free of low-degree…

二水平因子设计中抗趋势运行顺序的构造AI 解读

In experimental situations where a factorial design with all factors occurring at two levels is to be run in a time sequence, the usual advice given to the experimenter is that the order of runs should be randomized before the experiment is performed; however, randomization may lead to an undesirable run order. For example, in a factory experiment, there may be a certain learning process that occurs over time as a result of making level changes in the factors being studied,…

Kiefer–Wolfowitz 等价定理在哈达玛变换光学问题中的应用AI 解读

Let $\Omega = \{\mathbf{x} = (x_1, \cdots, x_n)^T: 0 \leq x_i \leq 1\}$ be the unit cube in $R^n$. For any probability measure $\xi$ on $\Omega$, let $\mathbf{M}(\xi) = \int_\Omega\mathbf{xx}^T \xi(d\mathbf{x})$. Harwit and Sloane (1976) conjectured that if $\mathbf{X}^\ast$ is the incidence matrix of a balanced incomplete block design (BIBD) with $n$ treatments and $n$ blocks of size $(n + 1)/2$, then $\mathbf{X}^\ast$ minimizes $\operatorname{tr}(\mathbf{X}^T\mathbf{X})^{-1}$…

调查抽样中的最优性准则AI 解读

This paper attempts to fill the gap between some different and conflicting approaches in survey sampling. Based on a fixed population regression-type model, a class of optimality criteria similar to those well accepted in optimal experimental design theory is introduced. The minimax and superpopulation approaches in survey sampling turn out to correspond to two extreme criteria in the proposed class. This helps understand the role of randomization. The strategy of simple…

调查抽样中的最优性准则AI 解读

SUMMARY This paper attempts to fill the gap between some different and conflicting approaches in survey sampling. Based on a fixed population regression-type model, a class of optimality criteria similar to those well accepted in optimal experimental design theory is introduced. The minimax and superpopulation approaches in survey sampling turn out to correspond to two extreme criteria in the proposed class. This helps understand the role of randomization. The strategy of…

抽样调查的极小极大方法AI 解读

Suppose that there is a population of $N$ identifiable units each with two associated values $x_i$ and $y_i$. All $N$ values of $x$ are given but $y_i$ is determined only after the $i$th unit is selected and observed. The objective is to estimate the population total $\sum^N_{i=1} y_i$. It is assumed that $y_i = \theta x_i + \delta_ig(x_i), 1 \leq i \leq N$, where $(\delta_1, \cdots, \delta_N)$ is in some bounded neighborhood of $(0, \cdots 0)$. The Rao-Hartley-Cochran and…