标题： 回归模型选择在一般条件下的研究 显示英文标题

标题： Regression Model Selection Under General Conditions

摘要： 模型选择准则统计学中最重要的工具之一。证明模型选择准则渐近最优的证明针对模型类型（线性回归、分位数回归、惩罚回归等）、估计方法（线性平滑器、最大似然、广义矩方法等）、数据类型（独立同分布、依赖数据、高维等）和模型选择准则类型进行了定制。此外，假设通常具有限制性且不现实，使得研究人员确定模型选择准则是否选择最优模型的过程缓慢而曲折。本文提供了通用的证明，在一般条件下展示了广泛范围内的模型选择准则的渐近最优性。本文不仅在渐近意义上验证了大多数情况下的模型选择准则，还统一并扩展了一系列之前不同的结果。 显示英文摘要

摘要： Model selection criteria are one of the most important tools in statistics. Proofs showing a model selection criterion is asymptotically optimal are tailored to the type of model (linear regression, quantile regression, penalized regression, etc.), the estimation method (linear smoothers, maximum likelihood, generalized method of moments, etc.), the type of data (i.i.d., dependent, high dimensional, etc.), and the type of model selection criterion. Moreover, assumptions are often restrictive and unrealistic making it a slow and winding process for researchers to determine if a model selection criterion is selecting an optimal model. This paper provides general proofs showing asymptotic optimality for a wide range of model selection criteria under general conditions. This paper not only asymptotically justifies model selection criteria for most situations, but it also unifies and extends a range of previously disparate results.