In this paper, using the shrinkage-based approach for portfolio weights and modern results from random matrix theory we construct an effective procedure for testing the efficiency of the expected utility (EU) portfolio and discuss the asymptotic behavior of the proposed test statistic under the high-dimensional asymptotic regime, namely when the number of assets $p$ increases at the same rate as the sample size $n$ such that their ratio $p/n$ approaches a positive constant $c\in (0,1)$ as $n\to \infty$ . We provide an extensive simulation study where the power function and receiver operating characteristic curves of the test are analyzed. In the empirical study, the methodology is applied to the returns of S&P 500 constituents.

中文翻译：

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高尺寸预期公用事业组合的统计推断

在本文中，使用基于收缩的投资组合权重方法和随机矩阵理论的现代结果，我们构建了一种有效的程序来测试预期效用（EU）投资组合的效率，并讨论了在高风险下拟议的测试统计量的渐近行为维渐近体制，即当资产数量 $ p $ 以与样本量相同的速度增加 $ n $ 这样他们的比例 $ p / n $ 接近正常数 $ c \ in（0,1）$ 如 $ n \ to \ infty $ 。我们提供了广泛的仿真研究，其中分析了测试的功率函数和接收器工作特性曲线。在实证研究中，该方法适用于标准普尔500成份股的收益。