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摘要翻译：
证明了在一类非辨识线性不适定逆模型中，基于谱正则化的估计收敛于结构参数的最佳逼近。重要的是，这种收敛性在一致和希尔伯特空间范数中成立。我们描述了当最佳近似与结构参数重合或至少合理近似时的几种情况，并讨论了我们的结果如何在部分辨识设置中有用。最后，我们证明了辨识失败对于正则化估计的线性泛函的渐近分布具有重要的意义，该正则化估计可以具有加权卡方分量。对各种高维和非参数IV回归进行了理论说明。
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英文标题：
《Is completeness necessary? Estimation in nonidentified linear models》
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作者：
Andrii Babii and Jean-Pierre Florens
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最新提交年份：
2021
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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：Economics 经济学
二级分类：Econometrics 计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Statistics 统计学
二级分类：Machine Learning 机器学习
分类描述：Covers machine learning papers (supervised, unsupervised, semi-supervised learning, graphical models, reinforcement learning, bandits, high dimensional inference, etc.) with a statistical or theoretical grounding
覆盖机器学习论文（监督，无监督，半监督学习，图形模型，强化学习，强盗，高维推理等）与统计或理论基础
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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 show that estimators based on spectral regularization converge to the best approximation of a structural parameter in a class of nonidentified linear ill-posed inverse models. Importantly, this convergence holds in the uniform and Hilbert space norms. We describe several circumstances when the best approximation coincides with a structural parameter, or at least reasonably approximates it, and discuss how our results can be useful in the partial identification setting. Lastly, we document that identification failures have important implications for the asymptotic distribution of a linear functional of regularized estimators, which can have a weighted chi-squared component. The theory is illustrated for various high-dimensional and nonparametric IV regressions.
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PDF链接：
https://arxiv.org/pdf/1709.03473
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