The use of the L-curve in the regularization of discrete ill-posed problems
SIAM Journal on Scientific Computing
A Technique for the Numerical Solution of Certain Integral Equations of the First Kind
Journal of the ACM (JACM)
A well-conditioned estimator for large-dimensional covariance matrices
Journal of Multivariate Analysis
Deblurring Images: Matrices, Spectra, and Filtering (Fundamentals of Algorithms 3) (Fundamentals of Algorithms)
Portfolio Selection with Robust Estimation
Operations Research
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Markowitz's portfolio selection problem chooses weights for stocks in a portfolio based on an estimated covariance matrix of stock returns. Our study proposes reducing noise in the estimation by using a Tikhonov filter function. In addition, we prevent rank deficiency of the estimated covariance matrix and propose a method for effectively choosing the Tikhonov parameter, which determines the filtering intensity. We put previous estimators into a common framework and compare their filtering functions for eigenvalues of the correlation matrix. We demonstrate the effectiveness of our estimator using stock return data from 1958 through 2007.