Portfolios constructed by the classical mean-variance model are very sensitive to outliers. We propose the use of a non-parametric estimation method based on statistical data depth functions. Specifically, we exploit the notion of the weighted $$L^{p}$$ depth function to obtain robust estimates of the mean and covariance matrix of the asset returns. This approach has the advantage to be independent of parametric assumptions, and less sensitive to changes in the asset return distribution than traditional techniques. The proposed procedure is evaluated and compared with standard and other robust techniques through simulated and real data. Results indicate effective improvements of the proposed method in terms of out-of-sample performance.

中文翻译：

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通过加权 $$L^{p}$$Lp 深度函数的稳健均值方差投资组合

由经典均值方差模型构建的投资组合对异常值非常敏感。我们建议使用基于统计数据深度函数的非参数估计方法。具体来说，我们利用加权 $$L^{p}$$ 深度函数的概念来获得资产收益的均值和协方差矩阵的稳健估计。这种方法的优点是独立于参数假设，并且与传统技术相比对资产收益分布的变化不太敏感。通过模拟和真实数据对建议的程序进行评估并与标准和其他稳健技术进行比较。结果表明，所提出的方法在样本外性能方面得到了有效改进。