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摘要翻译：
我们考虑了一个模型选择后估计量的无条件分布的估计问题。在这里，模型选择后估计器的概念是指首先选择一个模型（例如，通过像AIC这样的模型选择准则或通过假设检验过程），然后估计所选模型中的参数（例如，通过最小二乘或最大似然），所有这些都基于相同的数据集。我们证明了即使是渐近估计无条件分布也不可能有合理的精度。特别地，我们证明了该分布的任何估计量都不是一致相合的（甚至不是局部相合的）。这是分布估计器性能的（局部）极小极大下界的推论；在这里，性能是通过估计误差超过给定阈值的概率来衡量的。根据所考虑的情况，这些下限在大样本中显示接近1/2甚至1。对于模型选择后估计量的线性函数（例如，预测器）的分布也得到了类似的不可能性结果。
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英文标题：
《Can One Estimate The Unconditional Distribution of Post-Model-Selection
Estimators?》
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作者：
Hannes Leeb, Benedikt M. Poetscher
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
We consider the problem of estimating the unconditional distribution of a post-model-selection estimator. The notion of a post-model-selection estimator here refers to the combined procedure resulting from first selecting a model (e.g., by a model selection criterion like AIC or by a hypothesis testing procedure) and then estimating the parameters in the selected model (e.g., by least-squares or maximum likelihood), all based on the same data set. We show that it is impossible to estimate the unconditional distribution with reasonable accuracy even asymptotically. In particular, we show that no estimator for this distribution can be uniformly consistent (not even locally). This follows as a corollary to (local) minimax lower bounds on the performance of estimators for the distribution; performance is here measured by the probability that the estimation error exceeds a given threshold. These lower bounds are shown to approach 1/2 or even 1 in large samples, depending on the situation considered. Similar impossibility results are also obtained for the distribution of linear functions (e.g., predictors) of the post-model-selection estimator.
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PDF链接：
https://arxiv.org/pdf/704.1584
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