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高阶渐近理论与似然原则：单参数模型AI 解读

Inferences based on higher-order asymptotics, in contrast to those based on standard first-order methods, approximate exact inferences closely enough to depend on the reference set. We use this feature to quantify the effect of the reference set on exact inferences. In particular, the difference in P-values for two reference sets can be at most O(n−½), and it is seen that one can often identify the coefficient of n−½. Although this is useful from a foundational viewpoint,…

多参数指数族中高阶渐近方法的实践应用AI 解读

SUMMARY Recently developed asymptotics based on saddlepoint methods provide important practical methods for multiparameter exponential families, especially in generalized linear models. The aim here is to clarify and explore these. Attention is restricted to tests and confidence intervals regarding a single parametric function which can be represented as a natural parameter of a full rank exponential family. Excellent approximations to exact conditional inferences are often…

两样本位置问题的二元符号秩检验AI 解读

SUMMARY A signed rank affine invariant test for the difference in location between two elliptically symmetric populations is proposed. Asymptotic properties of the test are developed under the null hypothesis and under contiguous alternatives. The proposed statistic is compared with three of its competitors using Monte Carlo studies and Pitman asymptotic relative efficiencies. It is seen that the signed rank statistic introduced is especially powerful when the underlying…

单样本多元位置问题的符号秩检验AI 解读

An affine-invariant signed-rank test is proposed for the one-sample multivariate location problem. The test suggested is a modification of Randles's multivariate sign test based on interdirections, which extends Blumen's bivariate procedure to the multidimensional setting. Comparisons are made between the proposed statistic and several competitors via Pitman asymptotic relative efficiencies and Monte Carlo results. The signed-rank statistic appears to be robust. It performs…