This algorithm seeks to find a covariance (dense) estimate that (asymptotically) minimizes the mean-squared error (MSE) obtained by linear shrinkage problem as proposed by Ledoit and Wolf (LW). It is effectively a interpolation/mix of the sample ML estimate of the covariance matrix, S, and the most well-conditioned (and naive) estimate F = 1/p tr(S) I.
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The data matrix of size
The method of estimating the optimal interpolating parameter. The default is OAS.
The improved estimate using Rao-Blackwell theorem, abbreviated RBLW, and the oracle approximating shrinkage (OAS) are also implemented. The algorithm seeks a solution to the problem:
minimize E[ || Sigma_O - Sigma ||^2 ] w.r.t. rho
s.t. Sigma_O = (1-rho)*S + rho*F
using various methods The interpolated rho value used is always min(rho,1). More information can be found in the given reference.
p numeric matrix with two extra attributes giving
the used mixture (rho) and the method.
Ledoit, O., & Wolf, M. (2004). A well-conditioned estimator for large-dimensional covariance matrices. Journal of Multivariate Analysis, 88(2), 365-411. doi:10.1016/S0047-259X(03)00096-4
Chen, Y., & Wiesel, A. (2010). Shrinkage algorithms for MMSE covariance estimation. Signal Processing, IEEE, 58(734), 1-28. Methodology; Computation. http://arxiv.org/abs/0907.4698
Schafer, J., & Strimmer, K. (2005). A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics. Statistical Applications in Genetics and Molecular Biology, 4(1). http://www.stat.wisc.edu/courses/st992-newton/smmb/files/expression/shrinkcov2005.pdf
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