Computing the nearest correlation matrix—a problem from finance

By Nicholas John Higham. 2002

951 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

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Citations in the corpus

Nonparametric kernel estimators for image classification (2012, methodology): “We therefore symmetrize the estimated Gram matrix (by taking half the sum of it and its transpose), then project to the cone of positive semi-deﬁnite matrices by discarding any negative eigenvalues from its spectrum [9].”
Near-optimal sensor placements in Gaussian processes (2005, neutral): “In low dimensions, this problem can be treated as an instance of finding a positive semidefinite Toeplitz matrix that is closest to the empirical covariance in Frobenius norm (Higham, 2002).”
A Heuristic for Moment-Matching Scenario Generation (2003, background): “One such algorithm can be found in [5].”
Random Fields Simplified: Preserving Marginal Distributions, Correlations, and Intermittency, With Applications From Rainfall to Humidity (2020, background): “Furthermore, if these matrices are not positive definite, they can be corrected to fulfil this property (Higham, 2002).”
Multivariate elliptically contoured stable distributions: theory and estimation (2013, methodology): “This can be corrected by methods like those of Higham (2002).”
Semi‐Parametric Models for the Multivariate Tail Dependence Function – the Asymptotically Dependent Case (2008, methodology): “In that case, we can apply algorithm 3.3 in Higham (2002) to project the indefinite correlation matrix to the class of positive © Board of the Foundation of the Scandinavian Journal of Statistics 2008. semi-definite correlation matrices, say ÂÂ T = R̂; see Klüppelberg & Kuhn (2006) for details.”
Multi-channel Weighted Nuclear Norm Minimization for Real Color Image Denoising (2017, background): “Firstly, it is worthy to investigate new weight matrix beyond the diagonal form, such as the correlation form [33], to further improve the color image denoising performance.”
Support Distribution Machines (2012, methodology): “Therefore, we project this estimated Gram matrix back to the cone of positive semi-deﬁnite matrices using the alternating projection method presented in Higham (2002).”
Diagonal and Low-Rank Matrix Decompositions, Correlation Matrices, and Ellipsoid Fitting (2012, background): “In addition, the problem of projecting onto the set of (possibly low-rank) correlation matrices has enjoyed considerable interest in mathematical finance and numerical analysis in recent years [16].”
Robust High-Dimensional Precision Matrix Estimation (2014, background): “Maronna and Zamar [2002] propose a high-dimensional covariance estimator, an orthogonalized version of the Gnanadesikan-Kettenring estimate (OGK).”
The Composite Marginal Likelihood (CML) Inference Approach with Applications to Discrete and Mixed Dependent Variable Models (2014, methodology): “While the method has been suggested in the past under various pseudonyms such as quasi-likelihood (Hjort and Omre, 1994; Hjort and Varin, 2008), split likelihood (Vandekerkhove, 2005), and pseudolikelihood or marginal pseudo-likelihood (Molenberghs and Verbeke, 2005), Varin (2008) discusses reasons ”