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逻辑回归 ROC 曲线的高估问题AI 解读

Logistic regression is often used to find a linear combination of covariates which best discriminates between two groups or populations. The ROC, receiver operating characteristic, curve is a good way of assessing the performance of the resulting score, but using the same data both to fit the score and to calculate its ROC leads to an over‐optimistic estimate of the performance which the score would give if it were to be validated on a sample of future cases. The paper…

Summary Observational data are often analysed as if they had resulted from a controlled study, and yet the tacit assumption of randomness can be crucial for the validity of inference. We take some simple statistical models and supplement them by adding a parameter θ which reflects the degree of non-randomness in the sample. For a randomized study θ is known to be 0. We examine the profile log-likelihood for θ and the sensitivity of inference to small non-zero values of θ.…

基于核删失的局部似然AI 解读

SUMMARY By drawing an analogy with likelihood for censored data, a local likelihood function is proposed which gives more weight to observations near a region of interest in the sample space. Resulting methods can be used for assessing local departures from a parametric model, and for semiparametric density estimation. Some theory, and three examples, is given.

污染数据的二元回归模型AI 解读

SUMMARY The nature of outliers in the context of binary regression data is discussed. Resistant fitting procedures produce estimated regression coefficients which are numerically larger than maximum likelihood, implying the need for a shrinkage-type correction. A simple model which allows for a small number of the binary responses being misrecorded is proposed, and associated techniques for robust estimation and diagnostics developed.

回归预测值的交叉验证收缩AI 解读

SUMMARY Copas (1983) suggests that shrinkage of predictors can be related to the least squares slope of actual on predicted values in a new set of data. Considering multiple regression in a crossvalidatory setting, this shrinkage slope is approximated by an estimable function of the fitted residuals. Patterns of heteroscedasticity of residual variance can lead to more, or less, shrinkage of least squares. A new predictor using a nonparametric shrinkage multiplier is proposed.

回归收缩预测量对历史与未来数据差异的稳健性AI 解读

SUMMARY Copas (1983) investigates the shrinkage associated with prediction in the usual linear multiple regression model and proposes using Stein-type predictors which anticipate this shrinkage. Assuming that the first two (population) moments of the regressor variables associated with individuals for which predictions are to be made coincide with the first two (sample) moments of those in the construction sample, preshrunk predictors give a uniformly lower prediction mean…

Summary The fit of a regression predictor to new data is nearly always worse than its fit to the original data. Anticipating this shrinkage leads to Stein-type predictors which, under certain assumptions, give a uniformly lower prediction mean squared error than least squares. Shrinkage can be particularly marked when stepwise fitting is used: the shrinkage is then closer to that expected of the full regression rather than of the subset regression actually fitted. Preshrunk…

关于似然、贝叶斯方法与预设值偏好的一则评论AI 解读

As judged by large sample efficiency, one can make use of a preconceived value in a considerably less modest way than Bayes's theorem permits, provided one respects the likelihood function.

关于似然、贝叶斯与对预设值倾向的一则评论AI 解读

As judged by large sample efficiency, one can make use of a preconceived value in a considerably less modest way than Bayes's theorem permits, provided one respects the likelihood function.

柯西分布似然的单峰性AI 解读

Although the likelihood for the median of a Cauchy distribution with known scale is often multimodal, the joint likelihood for both location and scale parameters has exactly one point of maximum and at most one stationary point. The maximized likelihood function is therefore unimodal. It is also suggested that the likelihood for the location, when evaluated at the maximum likelihood estimate of the scale, is unimodal considerably more often than might have been anticipated…

柯西分布似然的单峰性AI 解读

Although the likelihood for the median of a Cauchy distribution with known scale is often multimodal, the joint likelihood for both location and scale parameters has exactly one point of maximum and at most one stationary point. The maximized likelihood function is therefore unimodal. It is also suggested that the likelihood for the location, when evaluated at the maximum likelihood estimate of the scale, is unimodal considerably more often than might have been anticipated…

经验贝叶斯方法与标准治疗的重复使用AI 解读

The fact that more is generally known about a standard treatment in a clinical trial than about the test treatment is exploited in empirical Bayes estimates based on the results of using the same standard in other trials. Such estimates are proposed for the case of dicho-tomous response, and discussed in terms of an example in cancer research.

线性函数关系问题中的似然曲面AI 解读

Summary In a recent paper, Solari has shown that no maximum likelihood solution exists in the linear functional relationship problem. When account is taken of the rounding-off errors in the observations, however, the appropriate likelihood function is bounded and a solution can be found which is approximately maximum likelihood, in the sense that the value of the likelihood at that solution is close to the global supremum. The novel form of this solution is shown and the…

经验贝叶斯方法与标准治疗的重复使用AI 解读

The fact that more is generally known about a standard treatment in a clinical trial than about the test treatment is exploited in empirical Bayes estimates based on the results of using the same standard in other trials. Such estimates are proposed for the case of dicho-tomous response, and discussed in terms of an example in cancer research.

复合决策与经验贝叶斯AI 解读

Summary The analysis of a sequence of decision problems of identical structure is considered, and the similarities and differences between the compound decision and empirical Bayes approaches explored. The paper includes a brief review of the literature and examines the criteria which have been used in comparing compound decision and empirical Bayes procedures with conventional methods. The performance of one of these procedures is examined in detail, and the previously…