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Bradley–Terry 配对比较模型中参数个数趋于无穷时的渐近理论AI 解读

We are concerned here with establishing the consistency and asymptotic normality for the maximum likelihood estimator of a “merit vector” $(u_0,\dots,u_t)$, representing the merits of $t +1$ teams (players, treatments, objects), under the Bradley–Terry model, as $t \to \infty$. This situation contrasts with the well-known Neyman–Scott problem under which the number of parameters grows with $t$ (the amount of sampling), and for which the maximum likelihood estimator fails…

平滑先验下 Wiener 过程漂移的序贯检验与热方程AI 解读

Methods are described which permit one to work with continuous-time optimal stopping problems, using the heat equation, even when the prior placed on the drift parameter of a Wiener process is not normal. The details of the method are worked out for Chernoff's problem of testing the sign of the drift parameter when the prior is "smooth."

二元响应临床试验模型的贝叶斯决策规则AI 解读

The risk in a trial to compare two medical treatments is borne by the patients who receive the inferior treatment during the experimental phase and by those remaining after the experiment who will all receive the inferior treatment if the results are misleading. The Bayes rule indicates, for the observed progression of successes and failures, when it is optimal to stop this experimental phase. This stopping rule can be described exactly, or nearly so, for symmetric two-point…

临床试验两阶段程序的极小极大风险AI 解读

SUMMARY The risk involved in a trial to compare two medical treatments is shared by patients who receive the inferior treatment during the experimental phase and those remaining after the experiment who might all receive the inferior treatment if the results are misleading. We consider the maximum of this risk with respect to the unknown probabilities of success and seek allocation rules that minimize this quantity, for a given total of patients. It needs extensive…

似然比随机序性质的扩展AI 解读

Extensions in two directions are described of the well-known stochastic ordering property of likelihood ratios. 1. It is shown that the stochastic ordering property holds in a very general conditional sense. 2. It is shown that, for the usual setting occurring in sequential analysis, sequences of likelihood ratios possess the same stochastic ordering property in a multivariate sense. Applications to sequential analysis, and elsewhere, are described.