论文检索

贝叶斯结构化线性模型的一般框架AI 解读

High dimensional statistics deals with the challenge of extracting structured information from complex model settings. Compared with a large number of frequentist methodologies, there are rather few theoretically optimal Bayes methods for high dimensional models. This paper provides a unified approach to both Bayes high dimensional statistics and Bayes nonparametrics in a general framework of structured linear models. With a proposed two-step prior, we prove a general oracle…

正态混合密度极大似然与贝叶斯估计的熵及收敛速度AI 解读

We study the rates of convergence of the maximum likelihood estimator (MLE) and posterior distribution in density estimation problems, where the densities are location or location-scale mixtures of normal distributions with the scale parameter lying between two positive numbers. The true density is also assumed to lie in this class with the true mixing distribution either compactly supported or having sub-Gaussian tails. We obtain bounds for Hellinger bracketing entropies…

回归函数单调性的检验AI 解读

We consider the problem of testing monotonicity of the regression function in a nonparametric regression model. We introduce test statistics that are functionals of a certain natural $U$-process. We study the limiting distribution of these test statistics through strong approximation methods and the extreme value theory for Gaussian processes. We show that the tests are consistent against general alternatives.

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.

摘要暂缺