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识别多项式回归次数的最优设计AI 解读

If an experimenter wants to determine the degree of a polynomial regression on the basis of a sample of observations, Anderson showed that the following method is optimal. Starting with the highest (specified) degree the procedure is to test in sequence whether the coefficients are 0. In this paper optimal designs for Anderson's procedure are determined explicitly. The optimal design maximizes the minimum power of a given set of alternatives.

紧区间上多项式回归的辨别设计AI 解读

In the polynomial regression model of degree $m \in \mathbb{N}$ we consider the problem of determining a design for the identification of the correct degree of the underlying regression. We propose a new optimality criterion which minimizes a weighted $p$-mean of the variances of the least squares estimators for the coefficients of $x^l$ in the polynomial regression models of degree $l = 1,\cdots, m$. The theory of canonical moments is used to determine the optimal designs…

加权多项式回归 E 最优设计的一则札记AI 解读

In a recent paper Pukelsheim and Studden determined the $E$-optimal design for the polynomial regression model on the interval $\lbrack - 1, 1\rbrack$ where the variances of different observations are assumed to be constant. In this note we show that these results can be generalized for polynomial regression models with non constant variances proportional to specific functions.

D 最优设计的 Elfving 定理AI 解读

We consider a model robust version of the $c$-optimality criterion minimizing a weighted product with factors corresponding to the variances of the least squares estimates for linear combinations of the parameters in different models. A generalization of Elfving's theorem is proved for the optimal designs with respect to this criterion by an application of an equivalence theorem for mixtures of optimality criteria. As a special case an Elfving theorem for the $D$-optimal…

双因素混合模型的秩方法AI 解读

The test problem of fixed treatment effects is considered in the two-factor mixed model with interaction and unequal cell frequencies when the classical assumptions of normality do not hold. An explicit form of a test statistic is derived using a partial rank transform (ranking all observations within each block), and the asymptotic distribution of the statistic is determined under the assumption that the number of blocks tends to infinity and the cell frequencies are…

双因素混合模型的秩检验方法AI 解读

The test problem of fixed treatment effects is considered in the two-factor mixed model with interaction and unequal cell frequencies when the classical assumptions of normality do not hold. An explicit form of a test statistic is derived using a partial rank transform (ranking all observations within each block), and the asymptotic distribution of the statistic is determined under the assumption that the number of blocks tends to infinity and the cell frequencies are…