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用图形识别回归异常值与混合结构AI 解读

Regressions in practice can include outliers and other unknown subpopulation structures. For example, mixtures of regressions occur if there is an omitted categorical predictor, like gender or location, and different regressions occur within each category. The theory of regression graphics based on central subspaces can be used to construct graphical solutions to long-standing problems of this type. It is argued that in practice the central subspace automatically expands to…

Digitised version produced by the EUI Library and made available online in 2020.

优选点几何与统计流形AI 解读

A new mathematical object called a preferred point geometry is introduced in order to (a) provide a natural geometric framework in which to do statistical inference and (b) reflect the distinction between homogeneous aspects (e.g., any point $\theta$ may be the true parameter) and preferred point ones (e.g., when $\theta_0$ is the true parameter). Although preferred point geometry is applicable generally in statistics, we focus here on its relationship to statistical…

基于剖面似然的区间估计：强拉格朗日理论及判别分析应用AI 解读

Strong Lagrangian theory is used to illuminate the properties of the profile log likelihood. General conditions are given which lead to a simplification of the computations required to plot this function or calculate interval estimates based upon it. The results presented are rather general with a variety of possible applications. In particular, it is shown that they provide a simple solution to the important practical problem of obtaining an interval estimate for the…

基于剖面似然的区间估计：强拉格朗日理论及判别应用AI 解读

Strong Lagrangian theory is used to illuminate the properties of the profile log likelihood. General conditions are given which lead to a simplification of the computations required to plot this function or calculate interval estimates based upon it. The results presented are rather general with a variety of possible applications. In particular, it is shown that they provide a simple solution to the important practical problem of obtaining an interval estimate for the…

主成分分析中的影响诊断AI 解读

In linear regression, the theoretical influence function and the various sample versions of it have an established place as diagnostic tools. These same functions are developed here to provide methods for the detection of influential observations in principal components analysis. The perturbation theory of real symmetric matrices unifies this development. Some interesting points of contrast with the regression case are noted and explained theoretically.

判别分析中的区间估计：多元正态等协方差情形AI 解读

A general approach to discrimination problems is described which emphasizes the viewpoint of individual cases and expresses the uncertainty with which individual decisions are made. It is applied to the particular case of two multivariate normal distributions with a common covariance matrix. An affine transformation, to which the key quantities are invariant, simplifies discussion of the distribution of the estimated log odds ratio and suggests a practically useful plot…

主成分分析中的影响诊断AI 解读

In linear regression, the theoretical influence function and the various sample versions of it have an established place as diagnostic tools. These same functions are developed here to provide methods for the detection of influential observations in principal components analysis. The perturbation theory of real symmetric matrices unifies this development. Some interesting points of contrast with the regression case are noted and explained theoretically.

判别分析中的区间估计：多元正态且协方差相等的情形AI 解读

A general approach to discrimination problems is described which emphasizes the viewpoint of individual cases and expresses the uncertainty with which individual decisions are made. It is applied to the particular case of two multivariate normal distributions with a common covariance matrix. An affine transformation, to which the key quantities are invariant, simplifies discussion of the distribution of the estimated log odds ratio and suggests a practically useful plot…

摘要暂缺

两个非中心 F 随机变量的协方差与估计线性判别函数的方差AI 解读

The covariance of two noncentral F random variables with a common covariance matrix is obtained from which the variance of their difference follows easily. An application of this latter result in discriminant analysis is then given.