摘要翻译：
我们提出了一个在时间相关（绝对正则混合）数据下M-估计问题的正则化的一般框架，它包含了许多现有的估计量。我们得到了正则M-估计的非渐近集中界。我们的结果显示了方差-偏差的权衡，方差项由参数集复杂性的新度量来控制。我们还表明混合结构通过缩放观测数目影响方差项；根据混合系数的衰减速率，这种标度甚至会影响渐近性态。最后，我们提出了一种数据驱动的方法来选择正则化估计器的调谐参数，该方法产生了与最优平衡（平方）偏差和方差项相同的（直到常数）集中界。我们用几个典型的例子来说明结果。
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英文标题：
《On the Non-Asymptotic Properties of Regularized M-estimators》
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作者：
Demian Pouzo
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最新提交年份：
2016
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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：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 propose a general framework for regularization in M-estimation problems under time dependent (absolutely regular-mixing) data which encompasses many of the existing estimators. We derive non-asymptotic concentration bounds for the regularized M-estimator. Our results exhibit a variance-bias trade-off, with the variance term being governed by a novel measure of the complexity of the parameter set. We also show that the mixing structure affect the variance term by scaling the number of observations; depending on the decay rate of the mixing coefficients, this scaling can even affect the asymptotic behavior. Finally, we propose a data-driven method for choosing the tuning parameters of the regularized estimator which yield the same (up to constants) concentration bound as one that optimally balances the (squared) bias and variance terms. We illustrate the results with several canonical examples.
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PDF链接：
https://arxiv.org/pdf/1512.06290