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协变量存在时两种异方差处理的最优设计AI 解读

Optimum designs are described for two treatments with different variances when covariates are included in the model. The designs, a generalization of Neyman allocation, are required in personalized medicine to model the effect of covariates on the choice of treatment. The use of the designs in clinical trials is indicated. D-optimality of the designs is established using results from Kiefer’s general equivalence theorem. The results are obtained with the use of surprisingly…

前向搜索中的附加变量t检验与被掩盖异常值对模型选择的影响AI 解读

Monitoring the t‐tests for individual regression coefficients in ‘forward’ search fails to identify the importance of observations to the significance of the individual regressors. This failure is due to the ordering of the data by the search. We introduce an added‐variable test which has the desired properties since the projection leading to residuals destroys the effect of the ordering. An example illustrates the effect of several masked outliers on model selection.…

异方差线性模型的 D 最优设计AI 解读

The methods of optimum experimental design are applied to models in which the variance, as well as the mean, is a parametric function of explanatory variables. Extensions to standard optimality theory lead to designs when the parameters of both the mean and the variance functions, or the parameters of only one function, are of interest. The theory also applies whether the mean and variance are functions of the same variables or of different variables, although the…

摘要暂缺

快速稳健的多重异常值检测方法AI 解读

A few repeats of a simple forward search from a random starting point are shown to provide sufficiently robust parameter estimates to reveal masked multiple outliers. The stability of the patterns obtained is exhibited by the stalactite plot. The robust estimators used are least median of squares for regression and the minimum volume ellipsoid for multivariate outliers. The forward search also has potential as an algorithm for calculation of these parameter estimates. For…

摘要暂缺

有先验信息时区分两个竞争模型的最优实验设计AI 解读

The design of experiments for discriminating between two rival models in the presence of prior information is analyzed. The method of Atkinson & Fedorov is extended. A theorem derived from the Kiefer-Wolfowitz General Equivalence Theorem is used to construct and check optimal designs. Some examples are provided.

回归变换中渐近等价检验统计量的比较AI 解读

A simulation comparison is made of six asymptotically equivalent test statistics for transformation of the response in regression; the tests typically have observed sizes up to twice the nominal size. A likelihood ratio statistic, a score statistic, and a Wald statistic behave very similarly, both at the null hypothesis and in terms of power. Values of all the statistics are highly positively correlated. The greater part of any differences between the statistics is…

回归响应变换中渐近等价检验统计量的比较AI 解读

A simulation comparison is made of six asymptotically equivalent test statistics for transformation of the response in regression; the tests typically have observed sizes up to twice the nominal size. A likelihood ratio statistic, a score statistic, and a Wald statistic behave very similarly, both at the null hypothesis and in terms of power. Values of all the statistics are highly positively correlated. The greater part of any differences between the statistics is…

图形、变换与回归：回归诊断图形方法导论AI 解读

This handbook provides a detailed, down-to-earth introduction to regression diagnostic analysis, a technique of growing importance for work in applied statistics. Heavily illustrated, with numerous examples to illuminate the discussion, this timely volume outlines methods for regression models, stressing detection of outliers and inadequate models; describes the transformation of variables in an equation, particularly the response; and considers such advanced topics as…

摘要暂缺

回归诊断、变换与构造变量AI 解读

Summary Two diagnostic displays for outlying and influential observations in multiple regression are reviewed. In some examples apparent outliers vanish after transformation of the data. Interpretation of the score statistic for transformations as regression on a constructed variable leads to partial residual plots for transformations and makes the two diagnostic displays available for detection of the influence of individual observations on the evidence for a…

Sichel 复合泊松分布的推断AI 解读

In a long-tailed compound Poisson distribution introduced by Sichel, the probabilities can only readily be calculated if one of the parameters λ has half-integer values, that is, λ = m + 1/2, m integer. The maximum likelihood estimation of this parameter is compared with an approximate method derived from a grid of half-integer values. It is found that the approximate method, which avoids excessive special computation, yields inferences indistinguishable from those based on…

回归异常观测与影响观测的两种图形诊断AI 解读

The paper describes two procedures for detecting observations with outlying values either in the response variable or in the explanatory variables in multiple regression. These procedures are presented as half normal plots with envelopes derived from simulation in order to avoid overinterpretation of the data. Analysis of a well-known data set leads to the use of a data transformation, a simple test for which is commended, and to some comments on the relationship with robust…

生成贝塔随机变量的一族切换算法AI 解读

An easily programmed algorithm is described for generating samples from the beta distribution for any allowable values of the parameters. The performance of the method is comparable with that of the best known algorithms for the different cases. As a result it is no longer necessary to have special algorithms depending upon whether neither, one or both of the parameters are less than one.

用于选择回归模型的后验概率AI 解读

A simple Bayesian formula for the posterior probability of one of several regression models is shown to be systematically misleading unless all models have the same number of parameters. Even in this case the use of improper priors leads to arbitrary inferences, as it does more generally. An alternative weighting for choosing a model is suggested and the relationship between significance tests and data-dependent priors mentioned.

用于回归模型选择的后验概率AI 解读

SUMMARY A simple Bayesian formula for the posterior probability of one of several regression models is shown to be systematically misleading unless all models have the same number of para- meters. Even in this case the use of improper priors leads to arbitrary inferences, as it does more generally. An alternative weighting for choosing a model is suggested and the relation- ship between significance tests and data-dependent priors mentioned. An alternative to the analysis of…

摘要暂缺

通过判别分析进行稳健回归AI 解读

For linear regression with grouped data, and with an equal number of observations per grouping point, linear discriminant analysis is applied to the ordered response variables to find that combination which shows strongest linear regression. After a modification to remove weights with an anomalous sign, there results a robust estimate of slope. Generalizations are outlined.

为检测回归模型不充分性而规划实验AI 解读

The adequacy of a regression model can be tested by fitting an extended model which reduces to the given model for particular parameter values. The choice of the extended model for nonlinear regression is discussed. Two experimental design criteria are compared and designs are developed for simultaneously providing information about both the original regression model and the hypothesis that the model is adequate. Designs are tabulated for detecting second-order departures…

线性 Logistic 与 Bradley–Terry 模型的检验AI 解读

A test is developed for the adequacy of the linear logistic model for binary data and is applied to the Bradley-Terry model for paired comparisons. The small-sample properties of the procedure are investigated for a numerical example.

线性Logistic模型与Bradley–Terry模型的检验AI 解读

A test is developed for the adequacy of the linear logistic model for binary data and is applied to the Bradley-Terry model for paired comparisons. The small-sample properties of the procedure are investigated for a numerical example.

为检出回归模型不充分性而设计实验AI 解读

The adequacy of a regression model can be tested by fitting an extended model which reduces to the given model for particular parameter values. The choice of the extended model for nonlinear regression is discussed. Two experimental design criteria are compared and designs are developed for simultaneously providing information about both the original regression model and the hypothesis that the model is adequate. Designs are tabulated for detecting second-order departures…