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簇相关误差线性模型的秩估计与相关推断AI 解读

R estimators based on the joint ranks (JR) of all the residuals have been developed over the last 20 years for fitting linear models with independently distributed errors. In this article, we extend these estimators to estimating the fixed effects in a linear model with cluster correlated continuous error distributions for general score functions. We discuss the asymptotic theory of the estimators and standard errors of the estimators. For the related mixed model with a…

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高崩溃点秩回归AI 解读

A weighted rank estimate is proposed that has 50% breakdown and is asymptotically normal at rate √n. Based on this theory, inferential procedures, including asymptotic confidence and tests, and diagnostic procedures, such as studentized residuals, are developed. The influence function of the estimate is derived and shown to be continuous and bounded everywhere in (x, Y) space. Examples show that robustness against outlying high-leverage clusters may approach that of the…

异方差线性模型的秩方法分析AI 解读

Heteroscedasticity often causes problems in the analysis of linear models. Frequently for such cases, scale is a function of the response. Here, for such models, a methodology is presented based on well-known rank-based procedures. The procedure is iterative. Using the residuals from an initial R estimate of the regression coefficients, scale is estimated by inverting a linear rank test for scale. This in turn leads to a weighted R estimate of the regression coefficients and…

异方差线性模型的秩方法分析AI 解读

Heteroscedasticity often causes problems in the analysis of linear models. Frequently for such cases, scale is a function of the response. Here, for such models, a methodology is presented based on well-known rank-based procedures. The procedure is iterative. Using the residuals from an initial R estimate of the regression coefficients, scale is estimated by inverting a linear rank test for scale. This in turn leads to a weighted R estimate of the regression coefficients and…

基于稳健估计的残差：使用与解释AI 解读

Residual plots and diagnostic techniques are important tools for examining the fit of a regression model. In the case of least squares fits, plots of residuals provide a visual assessment of the adequacy of various aspects of the fitted model. An important question is whether plots of robust residuals can be interpreted in the same manner as their least squares counterparts. This article addresses this problem for two popular classes of robust estimates: M estimates and GM…

多元线性模型的秩方法AI 解读

Rank-based methods are used to develop a theory for the multivariate linear model analogous to least squares. Quadratic procedures for testing H[β0β′]′K = 0 are considered both with and without the assumption of Symmetrie errors. When testing the hypothesis HβK = 0, the reduced-model R estimate is shown to be asymptotically a linear function of the full-model R estimate. Three asymptotically equivalent test procedures are developed: quadratic, aligned rank, and drop in…

基于秩的回归方法诊断AI 解读

Residual plots and diagnostic techniques have become important tools in examining the least squares fit of a linear model. In this article we explore the properties of the residuals from a rank-based fit of the model. We present diagnostic techniques that detect outlying cases and cases that have an influential effect on the rank-based fit. We show that the residuals from this fit can be used to detect curvature not accounted for by the fitted model. Furthermore, our…

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线性模型中基于秩的推断的几何解释AI 解读

Four different approaches, based on ranks, to testing hypotheses are unified through the geometry of the linear model. The various tests are identified with different but algebraically equivalent forms of the classical F test. Small sample differences are investigated via a Monte Carlo study using both rank and signed rank tests.

基于一步 R 估计的一般线性模型稳健分析AI 解读

Classical analysis of variance with least squares fitting is often used to discern structure in a linear model. McKean & Hettmansperger (1976) proposed a robust analysis based on ranks using the R-estimates proposed by Jaeckel (1972). These rank procedures depend on minimizing a dispersion surface and as a result are computationally restricted to small to moderate sized sets. In this paper we propose one step iterations based on a second derivative approximation to the…