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广义帕累托分布的数据拟合AI 解读

The generalized Pareto distribution (GPD) was introduced by Pickands to model exceedances over a threshold. It has since been used by many authors to model data in several fields. The GPD has a scale parameter ([sgrave] > 0) and a shape parameter (−∞ < k < ∞). The estimation of these parameters is not generally an easy problem. When k > 1, the maximum likelihood estimates do not exist, and when k is between 1/2 and 1, they may have problems. Furthermore, for k ≤ −1/2, second…

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寿命数据建模及其疲劳模型应用AI 解读

A new model for the analysis of lifetime data in the presence of a covariate is derived based on physical and statistical considerations. The model depends on five parameters that have clear physical interpretations. Two methods for the estimation of the parameters and of the quantiles are presented: one based on the order statistics and the other a regression estimator. The quantile estimators as well as the estimators of four of the five parameters are given in closed…

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多元样本离群值检测方法的一项修正AI 解读

SUMMARY We modify a method for identifying outliers in multivariate samples proposed by Hadi. A simulation study shows that this modification controls the size of the test, leads to substantially improved power and is more effective in dealing with the masking and swamping problems.

线性模型中多个离群点的识别程序AI 解读

We consider the problem of identifying and testing multiple outliers in linear models. The available outlier identification methods often do not succeed in detecting multiple outliers because they are affected by the observations they are supposed to identify. We introduce two test procedures for the detection of multiple outliers that appear to be less sensitive to this problem. Both procedures attempt to separate the data into a set of “clean” data points and a set of…

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多行观测对矩阵条件数影响的评估AI 解读

Given a matrix X of n observations on k variables, it is known that the singular values of X can change substantially when few rows are omitted from X. Hadi (1988) shows that no general closed-form equation can relate the singular values of X to the singular values of X with one row deleted and gives closed-form approximations to the relationship between the singular values of the two matrices. In this article, we extend Hadi's results to the more general case of…

评估多行观测对矩阵条件数的影响AI 解读

Given a matrix X of n observations on k variables, it is known that the singular values of X can change substantially when few rows are omitted from X. Hadi (1988) shows that no general closed-form equation can relate the singular values of X to the singular values of X with one row deleted and gives closed-form approximations to the relationship between the singular values of the two matrices. In this article, we extend Hadi's results to the more general case of…

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线性回归中的敏感性分析AI 解读

The Prediction Matrix Role of Variables in a Regression Equation Effects of an Observation on a Regression Equation Assessing the Influence of Multiple Observations Joint Impact of a Variable and an Observation Assessing the Effect of Errors of Measurements A Study of Model Sensitivity by the Generalized Linear Model Approach Computational Considerations. Appendix: Summary of Vector and Matrix Norms, Proofs of Three Theorems.