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指数族条件检验的渐近效率AI 解读

Let $P_\eta, \eta \in \Theta \times \Gamma \subset \mathbb{R} \times \mathbb{R}^k$, be an exponential family. It is shown that the sequence of tests $(\varphi^\ast_n)_{n\in\mathbb{N}}$, where $\varphi^\ast_n, n \in \mathbb{N}$, is u.m.p. in the class of all tests similar with respect to the nuisance-parameter $\gamma$ for the hypothesis $\{P^n_{(\theta, \gamma)}: \gamma \in \Gamma\}$ against alternatives $P^n_{(\theta_1, \eta_1)}, \theta_1 > \theta, \eta_1 \in \Gamma$, is…

强渐近中位数无偏估计量的渐近效率AI 解读

It is shown that the problem of asymptotic efficiency (in the Wolfowitz-sense) admits a satisfactory solution for the class of strongly asymptotically median unbiased estimators. The concept of strongly asymptotic median unbiasedness furthermore links up the classical approach (concerning estimator-sequences whose distribution functions converge) with Pfanzagl's concept of median unbiasedness.

后验分布的 Bernstein–von Mises 近似AI 解读

It is shown that under certain regularity conditions the Bernstein-v. Mises approximation of the posterior distributions is of order $O(n^{-\\frac{1}{2}})$ with high probability.