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杂论：二项回归误分类率的极大似然估计AI 解读

Binomial regression is commonly used to construct a binary classification rule from a set of observable covariates. The accuracy of the rule is summarised by empirical type 1 and type 2 misclassification rates as the threshold of the rule varies. However, the empirical misclassification rates are not the maximum likelihood estimators of the true rates if the binomial regression model is assumed true. We give a simple algorithm for the maximum likelihood estimators of the…

捕获概率随时间变化的再捕获实验中的精确枢轴量AI 解读

Testing and confidence interval construction for a parameter are achieved by constructing a pivotal. In this paper we study construction of approximate pivotals from recapture models where capture probabilities possibly vary from occasion to occasion. We compare the asymptotic standard normality of various pivotals including analogues of the classical maximum likelihood/Wald, score and likelihood ratio statistics. Some bias adjustments are developed and indicate that the…

The problem of estimating the number of binary responses that can be attributed to high levels of a continuous covariate is studied. The distribution of the covariate in the population is combined with the relative odds of response to produce a function, areas under which represent numbers of responses attributable to covariate values in that range. A combination of parametric and nonparametric smoothing is proposed. Consistent estimates of variance are developed as well as…