论文检索

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…

线性回归模型的贝叶斯最优设计AI 解读

A Bayesian version of Elfving's theorem is given for the $\mathbf{c}$-optimality criterion with emphasis on the inherent geometry. Conditions under which a one-point design is Bayesian $\mathbf{c}$-optimum are described. The class of prior precision matrices $R$ for which the Bayesian $\mathbf{c}$-optimal designs are supported by the points of the classical $\mathbf{c}$-optimal design is characterized. It is proved that the Bayesian $\mathbf{c}$-optimal design, for large $n,$…

关于多项式回归若干 φ_p 最优设计的注记AI 解读

In a recent paper of Gaffke an example was given regarding the $\phi_p$-optimal designs for the highest two coefficients in a one dimensional polynomial regression. The purpose of this paper is to supply a direct proof of this result using the theory of canonical moments and orthogonal polynomials.

q 维立方体上多元多项式回归的高效 D_s 最优设计AI 解读

Polynomial regression in $q$ variables of degree $n$ on the $q$-cube is considered. Approximate $D$-optimal and approximate $D_s$-optimal designs for estimating higher degree terms are investigated. Numerical results are given for $n = 2$ with arbitrary $q$ and for $n = 3, 4, 5$ and $q = 2, 3$. Exact solutions are given within the class of product designs together with some efficiency calculations.

利用典范矩构造三角回归与多项式回归的最优设计AI 解读

Consider a trigonometric regression of order $m$ or a polynomial regression of degree $m$. Explicit $D_s$-optimal designs are given for some subsets of the coefficients. Lauter type optimal designs are given for various models involving the order or the degree. The designs are calculated using canonical moments.

多项式回归中的若干稳健型 D 最优设计AI 解读

Consider a polynomial regression situation on an interval and also a robustness-type formulation of Stigler's. A technique involving canonical moments is discussed and some explicit solutions are given.

摘要暂缺

最小二乘与偏差最小化样条的渐近积分均方误差AI 解读

Let $S^d_k$ be the set of $d$th order splines on $\lbrack 0, 1 \rbrack$ having $k$ knots $\xi_1 < \xi_2 \cdots < \xi_k$. We consider the estimation of a sufficiently smooth response function $g$, using $n$ uncorrelated observations, by an element $s$ of $S^d_k$. For large $n$ and $k$ we have discussed the asymptotic behavior of the integrated mean square error (IMSE) for two types of estimators: (i) the least squares estimator and (ii) a bias minimizing estimator. The…

利用连分数构造多项式回归的 Ds 最优设计AI 解读

Consider a polynomial regression of degree $n$ on an interval. Explicit optimal designs are given for minimizing the determinant of the covariance matrix of the least squares estimators of the highest $s$ coefficients. The designs are calculated using continued fractions.

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.

多项式回归斜率估计的最优设计AI 解读

The problem of estimating the slope of a polynomial regression at a fixed point of the experimental region such that (a) the variance of the least-square estimate of the slope at the fixed point is a minimum and (b) the average variance of the least-square estimate of the slope is a minimum is discussed in this paper. In general these designs can be obtained using Kiefer-Wolfowitz [5] characterization of c-optimal designs, Federov [2] characterization of L-optimal designs,…