英文标题：
《Optimal Shrinkage Estimator for High-Dimensional Mean Vector》
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作者：
Taras Bodnar, Ostap Okhrin, Nestor Parolya
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最新提交年份：
2018
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英文摘要：
  In this paper we derive the optimal linear shrinkage estimator for the high-dimensional mean vector using random matrix theory. The results are obtained under the assumption that both the dimension $p$ and the sample size $n$ tend to infinity in such a way that $p/n \\to c\\in(0,\\infty)$. Under weak conditions imposed on the underlying data generating mechanism, we find the asymptotic equivalents to the optimal shrinkage intensities and estimate them consistently. The proposed nonparametric estimator for the high-dimensional mean vector has a simple structure and is proven to minimize asymptotically, with probability $1$, the quadratic loss when $c\\in(0,1)$. When $c\\in(1, \\infty)$ we modify the estimator by using a feasible estimator for the precision covariance matrix. To this end, an exhaustive simulation study and an application to real data are provided where the proposed estimator is compared with known benchmarks from the literature. It turns out that the existing estimators of the mean vector, including the new proposal, converge to the sample mean vector when the true mean vector has an unbounded Euclidean norm.
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中文摘要：
本文利用随机矩阵理论推导了高维均值向量的最优线性收缩估计。结果是在假设维度$p$和样本量$n$都趋于无穷大的情况下得到的，这样一来，$p/n到c在（0，infty）$。在对底层数据生成机制施加弱条件的情况下，我们找到了最优收缩强度的渐近等价物，并一致地估计了它们。本文提出的高维均值向量的非参数估计具有简单的结构，并且在概率为$1$的情况下，证明了当$c在（0,1）$时，该估计可以渐近地最小化二次损失。当（1，infty）$中的$c时，我们通过使用精度协方差矩阵的可行估计来修改估计量。为此，本文进行了详尽的模拟研究，并将所提出的估计量与文献中的已知基准进行了比较。结果表明，当真平均向量具有无界欧氏范数时，现有的平均向量估计量（包括新建议）收敛到样本平均向量。
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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：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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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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