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稀疏情形下若干多重检验程序的渐近贝叶斯最优性AI 解读

Within a Bayesian decision theoretic framework we investigate some asymptotic optimality properties of a large class of multiple testing rules. A parametric setup is considered, in which observations come from a normal scale mixture model and the total loss is assumed to be the sum of losses for individual tests. Our model can be used for testing point null hypotheses, as well as to distinguish large signals from a multitude of very small effects. A rule is defined to be…

混合分布递归估计的一致性AI 解读

Mixture models have received considerable attention recently and Newton [Sankhyā Ser. A 64 (2002) 306–322] proposed a fast recursive algorithm for estimating a mixing distribution. We prove almost sure consistency of this recursive estimate in the weak topology under mild conditions on the family of densities being mixed. This recursive estimate depends on the data ordering and a permutation-invariant modification is proposed, which is an average of the original over…

后验分布的收敛速率AI 解读

We consider the asymptotic behavior of posterior distributions and Bayes estimators for infinite-dimensional statistical models. We give general results on the rate of convergence of the posterior measure. These are applied to several examples, including priors on finite sieves, log-spline models, Dirichlet processes and interval censoring.

后验分布的收敛AI 解读

Z.A general (asymptotic) theory of estimation was developed by Ibragimov and Has’minskii under certain conditions on the normalized likelihood ratios. In an earlier work, the present authors studied the limiting behaviour of the posterior distributions under the general setup of Ibragimov and Has’minskii. In particular, they obtained a necessary condition for the convergence of a suitably centered (and normalized) posterior to a constant limit in terms of the limiting…

二阶 Pitman 接近性与 Pitman 可容许性AI 解读

Motivated by the first-order Pitman closeness of best asymptotically normal estimators and some recent developments on higher-order asymptotic efficiency of estimators, a second-order asymptotic theory is developed for comparison of estimators under the Pitman closeness criterion, covering both the cases without and with nuisance parameters. The notion of second-order Pitman admissibility is also developed.