英文标题：
《Tests for the weights of the global minimum variance portfolio in a
high-dimensional setting》
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作者：
Taras Bodnar, Solomiia Dmytriv, Nestor Parolya and Wolfgang Schmid
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最新提交年份：
2019
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英文摘要：
In this study, we construct two tests for the weights of the global minimum variance portfolio (GMVP) in a high-dimensional setting, namely, when the number of assets $p$ depends on the sample size $n$ such that $\\frac{p}{n}\\to c \\in (0,1)$ as $n$ tends to infinity. In the case of a singular covariance matrix with rank equal to $q$ we assume that $q/n\\to \\tilde{c}\\in(0, 1)$ as $n\\to\\infty$. The considered tests are based on the sample estimator and on the shrinkage estimator of the GMVP weights. We derive the asymptotic distributions of the test statistics under the null and alternative hypotheses. Moreover, we provide a simulation study where the power functions and the receiver operating characteristic curves of the proposed tests are compared with other existing approaches. We observe that the test based on the shrinkage estimator performs well even for values of $c$ close to one.
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中文摘要：
在这项研究中，我们构建了高维环境下全局最小方差投资组合（GMVP）权重的两个测试，即当资产数量$p$取决于样本大小$n$，使得$n$趋于无穷大时，从$\\ frac{p}{n}到c（0,1）$。在秩等于$q$的奇异协方差矩阵的情况下，我们假设（0，1）$中的$q/n到{c}作为$n到{infty$。所考虑的测试基于GMVP权重的样本估计量和收缩估计量。我们推导了在零假设和替代假设下检验统计量的渐近分布。此外，我们还提供了一个仿真研究，将所提出测试的功率函数和接收机工作特性曲线与其他现有方法进行了比较。我们观察到，基于收缩估计器的测试即使对于接近1加元的值也表现良好。
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分类信息：

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：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：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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