论文检索

通过参数逆回归估计回归的结构维数AI 解读

Summary A new estimation method for the dimension of a regression at the outset of an analysis is proposed. A linear subspace spanned by projections of the regressor vector X, which contains part or all of the modelling information for the regression of a vector Y on X, and its dimension are estimated via the means of parametric inverse regression. Smooth parametric curves are fitted to the p inverse regressions via a multivariate linear model. No restrictions are placed on…

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…

二元响应回归中的降维AI 解读

The idea of dimension reduction without loss of information can be quite helpful for guiding the construction of summary plots in regression without requiring a prespecified model. Focusing on the central subspace, we investigate such “sufficient” dimension reduction in regressions with a binary response. Three existing methods—sliced inverse regression, principal Hessian direction, and sliced average variance estimation—and one new method—difference of covariances—are…

摘要暂缺

广义线性模型中的偏残差图AI 解读

In this article we explore the structure and usefulness of partial residual plots as tools for visualizing curvature as a function of selected predictors x 2 in a generalized linear model (GLM), where the vector of predictors x is partitioned as x T = (x T 1, x T 2). The GLM extension of ceres plots is discussed, but to a lesser extent. The usefulness of these plots for obtaining a good visual impression of curvature may be limited by the specified GLM, the link function,…

评估回归模型适切性的图形方法AI 解读

Graphical paradigms for assessing the adequacy of nearly any regression model are discussed. The fundamental idea is to examine the fit of a model using a sequence of marginal model plots. On each plot, nonparametric estimates of fit derived from the model are compared to nonparametric fits based on the observed data. Several examples are given.

二元响应回归的图形方法AI 解读

Central dimension-reduction subspaces, which characterize the dependence of a response variable on one or more predictors, are developed and then used to guide the construction and interpretation of graphics for regression problems with a binary response variable. Graphical methods requiring neither a link function nor residuals are suggested for both development and criticism of model components implied by the central dimension-reduction subspace.

回归图形分析导论AI 解读

This article, which is based on an Interface tutorial, presents an overview of regression graphics, along with an annotated bibliography.The intent is to discuss basic ideas and issues without delving into methodological or theoretical details, and to provide a guide to the literature.

通过响应变量变换实现回归线性化AI 解读

We consider the problem of choosing a transformation t(y) of a univariate response variable y so that the regression function E{t(y)| x}is linear in the predictor vector x. Let y^ be the fitted values from a linear regression of y on x. Given a few simple assumptions, we show that the plot with y on the horizontal axis and y^ on the vertical axis can be used to visualise the needed transformation t(y). A smoother can then be used as an aid to assessing t(y) visually.

通过重加权使回归协变量呈椭圆对称分布AI 解读

We investigate a method of constructing weights to induce elliptically contoured covariates in regression analyses. Much recent work in regression has identified various data analytic and model robustness advantages associated with such covariates. In particular, new estimation methods like SIR, SIRII, SAVE, and PHD have been built around the assumption of elliptically contoured covariates. Finite samples of regression covariates may deviate from this ideal in practice, and…

回归图的解释AI 解读

A framework is developed for the interpretation of regression plots, including plots of the response against selected covariates, residual plots, added-variable plots, and detrended added-variable plots. It is shown that many of the common interpretations associated with these plots can be misleading. The framework also allows for the generalization of standard plots and the development of new plotting paradigms. A paradigm for graphical exploration of regression problems is…

通过响应变量变换实现回归线性化AI 解读

We consider the problem of choosing a transformation t(y) of a univariate response variable y so that the regression function E{t(y)| x}is linear in the predictor vector x. Let y^ be the fitted values from a linear regression of y on x. Given a few simple assumptions, we show that the plot with y on the horizontal axis and y^ on the vertical axis can be used to visualise the needed transformation t(y). A smoother can then be used as an aid to assessing t(y) visually.

异方差 G 最优设计AI 解读

SUMMARY This paper addresses the issue of constructing large sample G-optimal designs when the variability of the response varies across a compact design space. A useful characterization theorem is presented along with a computer algorithm for generating (heteroscedastic) G-optimal designs. to facilitate comparisons between D- and G-optimal designs, Atwood's inequality for comparing D- and G-efficiencies in homoscedastic models is generalized to heteroscedastic models. Some…

统计理论与建模：纪念 David Cox 爵士AI 解读

Part 1 Statistical theory - theoretical concepts significance tests theory of optimal tests estimation asymptotic theory. Part 2 Applied statistics - preliminary considerations statistical models statistical inference model adequancy exploratory and robust methods multi-variate methods use of computers. Part 3 Generalized linear models - a class of non-linear regression models likelihood functions estimation analysis of deviance checking the model. Part 4 Residuals and…

非线性回归中的杠杆、局部影响与曲率AI 解读

The connections between measures of leverage, statistical curvature, and the local influence of a mean-shift perturbation are explored in nonlinear regression models. The circumstances under which the Jacobian leverage reduces to a commonly-used linear approximation are found to be connected to the effective residual curvature of the nonlinear model. The local influence of a mean-shift perturbation in the model function is seen to be closely related to the Jacobian leverage.

非线性回归中的杠杆值、局部影响与曲率AI 解读

The connections between measures of leverage, statistical curvature, and the local influence of a mean-shift perturbation are explored in nonlinear regression models. The circumstances under which the Jacobian leverage reduces to a commonly-used linear approximation are found to be connected to the effective residual curvature of the nonlinear model. The local influence of a mean-shift perturbation in the model function is seen to be closely related to the Jacobian leverage.

非线性回归中的杠杆值与超杠杆AI 解读

Several measures of the leverage of an observation in a nonlinear regression model are defined and developed. In contrast to the upper bound on the leverage in a linear model, it is found that in a nonlinear model the leverage of an observation may exceed 1. Such a case is said to exhibit superleverage. Relationships between the leverage measures are explored, and several examples are developed to illustrate the proposed methodology.

摘要暂缺

摘要暂缺

评估后验影响的图形化个案统计量AI 解读

A single number summary of the influence of an observation on the posterior of the parameter of interest is useful, but does not convey all aspects of the effect of deleting the observation. We propose a plot that does convey all the effects of an observation on the posterior.

指数族非线性模型中正态近似准确性的诊断AI 解读

Diagnostics are investigated for assessing the agreement between likelihood and standard large-sample confidence regions for parameters from an exponential family nonlinear model (Cordeiro and Paula 1989). The development connects the contour methods proposed by Hodges (1985, 1987) with the curvature measures for normal, nonlinear regression proposed by Bates and Watts (1980) and Jennings's (1982, 1986) diagnostics for logistic regression. The proposed methodology is…

指数族非线性模型中正态近似准确性的诊断AI 解读

Diagnostics are investigated for assessing the agreement between likelihood and standard large-sample confidence regions for parameters from an exponential family nonlinear model (Cordeiro and Paula 1989). The development connects the contour methods proposed by Hodges (1985, 1987) with the curvature measures for normal, nonlinear regression proposed by Bates and Watts (1980) and Jennings's (1982, 1986) diagnostics for logistic regression. The proposed methodology is…

《揭示多元异常值与杠杆点》：评论AI 解读

Detecting outliers in a multivariate point cloud is not trivial, especially when there are several outliers. The classical identification method does not always find them, because it is based on the sample mean and covariance matrix, which are themselves affected by the outliers. To avoid this masking effect, we propose to compute distances based on very robust estimates of location and covariance. In the case of regression data, the outliers also may be unmasked by using a…

非线性回归中的置信曲线AI 解读

Standard Wald confidence regions for parameters in a normal nonlinear regression model often fail to capture accurately the uncertainty of estimation as reflected by the corresponding profile log-likelihood. We present a graphical method, along with a stable computational algorithm, for inference on scalar parameters in a nonlinear regression model.