Maaz Mahadi, Tarig Ballal, Muhammad Moinuddin, Tareq Y. Al-Naffouri, Ubaid Al-Saggaf
arXiv 12 Apr 2022 · eess.SP · publishedIEEE Access (2022) · 3 citations (OpenAlex)
arXiv:2204.05611 · PDF · DOI · OpenAlex · Extracted main text
This paper is concerned with optimizing the global minimum-variance portfolio's (GMVP) weights in high-dimensional settings where both observation and population dimensions grow at a bounded ratio. Optimizing the GMVP weights is highly influenced by the data covariance matrix estimation. In a high-dimensional setting, it is well known that the sample covariance matrix is not a proper estimator of the true covariance matrix since it is not invertible when we have fewer observations than the data dimension. Even with more observations, the sample covariance matrix may not be well-conditioned. This paper determines the GMVP weights based on a regularized covariance matrix estimator to overcome the aforementioned difficulties. Unlike other methods, the proper selection of the regularization parameter is achieved by minimizing the mean-squared error of an estimate of the noise vector that accounts for the uncertainty in the data mean estimation. Using random-matrix-theory tools, we derive a consistent estimator of the achievable mean-squared error that allows us to find the optimal regularization parameter using a simple line search. Simulation results demonstrate the effectiveness of the proposed method when the data dimension is larger than the number of data samples or of the same order.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Esa Ollila and Elias Raninen (2019) Optimal shrinkage covariance matrix estimation under random sampling from elliptical distributions | 0.874 | 5 | 2 | 100% |
| 2 | Liusha Yang, Romain Couillet, and Matthew R McKay (2015) A robust statistics approach to minimum variance portfolio optimization | 0.843 | 3 | 3 | 100% |
| 3 | Olivier Ledoit and Michael Wolf (2004) A well-conditioned estimator for large-dimensional covariance matrices | 0.811 | 4 | 2 | 100% |
| 4 | Francisco Rubio, Xavier Mestre, and Daniel P Palomar (2012) Performance analysis and optimal selection of large minimum variance portfolios under estimation risk | 0.737 | 3 | 2 | 100% |
| 5 | Amin Zollanvari and Edward R Dougherty (2015) Generalized consistent error estimator of linear discriminant analysis | 0.644 | 2 | 2 | 100% |
| 6 | Khalil Elkhalil, Abla Kammoun, Romain Couillet, Tareq Y Al-Naffouri,… (2020) A large dimensional study of regularized discriminant analysis self | 0.644 | 2 | 2 | 100% |
| 7 | S Chandrasekaran, GH Golub, M Gu, and Ali H Sayed (1998) Parameter estimation in the presence of bounded data uncertainties | 0.585 | 3 | 1 | 100% |
| 8 | Romain Couillet and Mérouane Debbah (2012) Signal processing in large systems: A new paradigm | 0.511 | 2 | 1 | 100% |
| 9 | Esa Ollila and Elias Raninen Matlab regularizedscm toolbox version 1.0 | 0.511 | 2 | 1 | 100% |
| 10 | Harry Markowitz (1952) Portfolio selection | 0.405 | 1 | 1 | 100% |
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