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回归中的k统计量与离散程度效应AI 解读

By the term $k$-statistic or polykay, we mean an unbiased estimate of a cumulant or product of cumulants [Fisher (1929) and Tukey (1950), 1956)]. In this paper, two sets of unbiased estimates are given for the case where the mean response, $E(Y)$, depends linearly on known covariates $x$. The $k$'s are symmetric functions of the least-squares residuals and have previously been discussed by Anscombe (1961; 1981, Appendix 2). The $l$'s are optimal in the sense of having…

评估 Logistic 回归模型的图形方法AI 解读

In ordinary linear regression, graphical diagnostic displays can be very useful for detecting and examining anomalous features in the fit of a model to data. For logistic regression models, the discreteness of binary data makes it difficult to interpret such displays. Modifications and extensions of linear model displays lead to three methods for diagnostic checking of logistic regression models. Local mean deviance plots are useful for detecting overall lack of fit.…

Logistic 回归诊断AI 解读

A maximum likelihood fit of a logistic regression model (and other similar models) is extremely sensitive to outlying responses and extreme points in the design space. We develop diagnostic measures to aid the analyst in detecting such observations and in quantifying their effect on various aspects of the maximum likelihood fit. The elements of the fitting process which constitute the usual output (parameter estimates, standard errors, residuals, etc.) will be used for this…

识别具有重要影响的离群观测AI 解读

Summary A method is proposed for examining a linear model for the presence of one or more important outliers—deviant observations which have a potentially large influence on the resulting parameter estimates. For this purpose, a new statistic is proposed and its distributional properties are discussed. The method itself is exploratory in nature, but exact significance tests are available. Several examples illustrate the method. Computational aspects are discussed.