英文标题:
《On the Strong Convergence of the Optimal Linear Shrinkage Estimator for
Large Dimensional Covariance Matrix》
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作者:
Taras Bodnar, Arjun K. Gupta and Nestor Parolya
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最新提交年份:
2014
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英文摘要:
In this work we construct an optimal linear shrinkage estimator for the covariance matrix in high dimensions. The recent results from the random matrix theory allow us to find the asymptotic deterministic equivalents of the optimal shrinkage intensities and estimate them consistently. The developed distribution-free estimators obey almost surely the smallest Frobenius loss over all linear shrinkage estimators for the covariance matrix. The case we consider includes the number of variables $p\\rightarrow\\infty$ and the sample size $n\\rightarrow\\infty$ so that $p/n\\rightarrow c\\in (0, +\\infty)$. Additionally, we prove that the Frobenius norm of the sample covariance matrix tends almost surely to a deterministic quantity which can be consistently estimated.
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中文摘要:
本文构造了高维协方差矩阵的最优线性收缩估计。随机矩阵理论的最新结果允许我们找到最佳收缩强度的渐近确定性等价物,并一致地估计它们。在协方差矩阵的所有线性收缩估计中,所发展的无分布估计几乎肯定服从最小的Frobenius损失。我们考虑的情况包括变量数量$p\\rightarrow\\infty$和样本大小$n\\rightarrow\\infty$,因此$p/n\\rightarrow c\\在(0,+\\infty)$中。此外,我们还证明了样本协方差矩阵的Frobenius范数几乎肯定趋向于一个可以一致估计的确定量。
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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:Mathematics 数学
二级分类:Probability 概率
分类描述:Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用:例如中心极限定理,大偏差,随机微分方程,统计力学模型,排队论
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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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