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二元极值的非参数贝叶斯推断AI 解读

Summary The tail of a bivariate distribution function in the domain of attraction of a bivariate extreme value distribution may be approximated by that of its extreme value attractor. The extreme value attractor has margins that belong to a three-parameter family and a dependence structure which is characterized by a probability measure on the unit interval with mean equal to 12, which is called the spectral measure. Inference is done in a Bayesian framework using a censored…

有界正态均值的极大似然估计改进AI 解读

We consider the problem of estimating the mean of a $p$-variate normal distribution with identity covariance matrix when the mean lies in a ball of radius $m$. It follows from general theory that dominating estimators of the maximum likelihood estimator always exist when the loss is squared error. We provide and describe explicit classes of improvements for all problems $(m, p)$. We show that,for small enough $m$, a wide class of estimators, including all Bayes estimators…

具有半空间形状的置信集AI 解读

SUMMARY For the problem of estimating the mean of a p-dimensional normal distribution, p > 1, confidence regions based on half-spaces bounded by a hyperplane having the vector of observations as normal are proposed. Confidence regions with exact probability of coverage are constructed. Tables are provided.