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As an addition to the already rich answers, I would suggest you to read the following paper by Marcos L. De Prado on the computation of Forward-Looking Correlation Matrices. Estimation of Theory-Implied Correlation Matrices https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3484152


The Ledoit-Wolf estimate cited by @develarist can be quite good, but as you say you already knew about "shrinking". It takes the population of correlations observed as an effective Bayesian prior for any given correlation, so it sort of inherently assumes that all pairs are similar an some sense. It would not work well, say, with known block sets of highly ...


Quantile regression is considered a robust procedure but lacks the quality of being fully differentiable. There are also regularized regression models like ridge regression, lasso regression and elastic net regression that implicitly consider the covariance of the data like OLS, but additionally reduce volatility in estimates through the introduction of bias....


You will have to add some constraints to get the weight vector of the eigen vector of the smallest eigen values, otherwise 0 is a trivial solution. Without going in the details of handling those extra constraints, the reason why the vector space associated with the smallest eigen value is relevant is because if you express variance of your portfolio in the ...

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