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数值型成对比较数据的最小二乘估计AI 解读

Abstract Least square estimators for graphical models for cardinal paired comparison data with and without covariates are rigorously analysed. Novel, graph-based, necessary, and sufficient conditions that guarantee strong consistency, asymptotic normality, and the exponential convergence of the estimated ranks are emphasized. A complete theory for models with covariates is laid out. In particular, conditions under which covariates can be safely omitted from the model are…

线性随机序与多元有序分布的定向推断AI 解读

Researchers are often interested in drawing inferences regarding the order between two experimental groups on the basis of multivariate response data. Since standard multivariate methods are designed for two sided alternatives they may not be ideal for testing for order between two groups. In this article we introduce the notion of the linear stochastic order and investigate its properties. Statistical theory and methodology are developed to both estimate the direction which…

基于序数优势曲线的随机有序分布推断AI 解读

Summary In a variety of applications researchers collect data that are sampled under ordered experimental conditions. In such situations it is reasonable to assume that outcomes are ordered stochastically by the level of the treatment. For example a toxicologist may want to assess the effect of a toxin on the reproductive system by studying the number of offspring produced by an animal as a function of the dose that it received. A variety of scientific questions arise in…