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重新考察泊松复合决策问题AI 解读

The compound decision problem for a vector of independent Poisson random variables with possibly different means has a half-century-old solution. However, it appears that the classical solution needs smoothing adjustment. We discuss three such adjustments. We also present another approach that first transforms the problem into the normal compound decision problem. A simulation study shows the effectiveness of the procedures in improving the performance over that of the…

高维正态均值向量估计的非参数经验贝叶斯与复合决策方法AI 解读

We consider the classical problem of estimating a vector μ=(μ1, …, μn) based on independent observations Yi∼N(μi, 1), i=1, …, n. Suppose μi, i=1, …, n are independent realizations from a completely unknown G. We suggest an easily computed estimator μ̂, such that the ratio of its risk E(μ̂−μ)2 with that of the Bayes procedure approaches 1. A related compound decision result is also obtained. Our asymptotics is of a triangular array; that is, we allow the distribution G to…

最优子集选择、高维统计学习的持续性与 l1 约束优化AI 解读

Let (Y, X1, …, Xm) be a random vector. It is desired to predict Y based on (X1, …, Xm). Examples of prediction methods are regression, classification using logistic regression or separating hyperplanes, and so on. We consider the problem of best subset selection, and study it in the context m=nα, α>1, where n is the number of observations. We investigate procedures that are based on empirical risk minimization. It is shown, that in common cases, we should aim to find the…

回归模型选择的渐近极小极大遗憾规则与维数惩罚AI 解读

This paper addresses the topic of model selection in regression.We emphasize the case of two models, testing which model provides a better prediction based on $n$ observations. Within a family of selection rules, based on maximizing a penalized log-likelihood under a normal model, we search for asymptotically minimax rules over a class $\mathscr{G}$ of possible joint distributions of the explanatory and response variables. For the class $\mathscr{G}$ of multivariate normal…