# Scov: Shrinkage covariance estimation In AEBilgrau/correlateR: Fast correlations and covariances

## Description

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.

## Usage

 ```1 2 3``` ```Scor(X, method = c("OAS", "RBLW", "LW", "SS")) Scov(X, method = c("OAS", "RBLW", "LW", "SS")) ```

## Arguments

 `X` The data matrix of size `n` by `p`. `method` The method of estimating the optimal interpolating parameter. The default is OAS.

## Details

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.

## Value

A `p` by `p` numeric matrix with two extra attributes giving the used mixture (rho) and the method.

## References

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

## Examples

 ```1 2 3 4 5 6``` ```n <- 3 X <- createData(n, 5) cov(X) Scov(X, method = "OAS") Scov(X, method = "RBLW") Scov(X, method = "LW") ```

AEBilgrau/correlateR documentation built on Dec. 27, 2018, 2:32 a.m.