论文检索

信息矩阵奇异时的最优设计测度AI 解读

The problem of establishing a useful necessary and sufficient condition for a design measure with singular information matrix to be Ds-optimal is well known. In this paper a sufficient condition involving a certain type of g-inverse is established for a more general convex criterion function to be minimized by such a design measure. The condition is necessary for DA-optimality and for a linear criterion function. There is some discussion about its necessity in general.

信息矩阵奇异时的最优设计测度AI 解读

The problem of establishing a useful necessary and sufficient condition for a design measure with singular information matrix to be Ds-optimal is well known. In this paper a sufficient condition involving a certain type of g-inverse is established for a more general convex criterion function to be minimized by such a design measure. The condition is necessary for DA-optimality and for a linear criterion function. There is some discussion about its necessity in general.

摘要暂缺

利用既有观测的最优回归设计AI 解读

A method is developed for constructing D-optimal designs in a linear regression context with k explanatory variables, when previous observations are available and a fixed number of new sets of values of the explanatory variables are to be chosen within the unit sphere. The effect of previous observations on the relationship between D-optimality and E-opti-mality is discussed. The relationship between designs constructed sequentially to be optimum for each new set of values…

利用既有观测的最优回归设计AI 解读

A method is developed for constructing D-optimal designs in a linear regression context with k explanatory variables, when previous observations are available and a fixed number of new sets of values of the explanatory variables are to be chosen within the unit sphere. The effect of previous observations on the relationship between D-optimality and E-opti-mality is discussed. The relationship between designs constructed sequentially to be optimum for each new set of values…

多重共线性与估计不精确AI 解读

Summary For the standard linear model containing several explanatory variables, the precision of estimation of linear parametric functions is analysed in terms of latent roots and vectors of X'X, where X is the matrix of values of explanatory variables. This analysis provides a practical method for detecting multicollinearity, and it is demonstrated that it is also useful in solving problems of optimum choice of new values of explanatory variables.

一般凸损失下回归问题的最优设计AI 解读

The polynomial regression model in which the errors are independent and identically distributed, is considered, and attention is focused on the estimate of β8, the coefficient, of the term of highest degree. A design D is a set of n values in [−1, 1] of the concomitant, variable x, and the least-squares estimator of β8, when the design D is used, is donoted by β(D). Then D* is said to dominate D if, for every continuous convex function c, E[c{β(D*)})≤= E[c{β(D)}. Does there…

一般凸损失下回归问题的最优设计AI 解读

The polynomial regression model in which the errors are independent and identically distributed, is considered, and attention is focused on the estimate of β8, the coefficient, of the term of highest degree. A design D is a set of n values in [−1, 1] of the concomitant, variable x, and the least-squares estimator of β8, when the design D is used, is donoted by β(D). Then D* is said to dominate D if, for every continuous convex function c, E[c{β(D*)})≤= E[c{β(D)}. Does there…

随机变量的关联与 Radon–Nikodym 导数的离散程度AI 解读

S. M. Ali, S. D. Silvey; Association between Random Variables and the Dispersion of a Radon–Nikodym Derivative, Journal of the Royal Statistical Society Se

随机变量的关联与 Radon–Nikodym 导数的离散程度AI 解读

Summary In a previous paper by one of the authors (Silvey, 1964) it was suggested that the Radon–Nikodym derivative of the joint distribution of two, not necessarily real-valued, random variables with respect to the product of their marginal distributions provides the analytic key for discussing association between the random variables. In this paper we shall develop this point and lend some support to the suggestion by proving that in the case of normal random vectors the…

相依随机变量情形下最大似然法的一则说明AI 解读

SUMMARY The validity of certain statistical procedures depends on the “classical” properties of the method of maximum-likelihood, viz., its consistency and the fact that it leads to an estimator whose asymptotic variance can be derived easily from the likelihood function. These properties are well established for the case where successive observations are independent. Here it is shown that their extension to the dependent case involves suitable behaviour of two…

最大似然估计程序及其配套显著性检验AI 解读

Summary The essence of many statistical problems, including most standard techniques, is to test whether or not the unknown parameters of an appropriate statistical model satisfy certain restrictions; and the outcome of such a test dictates whether it is necessary to provide estimates of these parameters which also satisfy the restrictions. In this paper we discuss and illustrate the relative merits, as practical tools for the consulting statistician, of two large-sample…

摘要暂缺

摘要暂缺