adapt the quick start in the README following PR #18; closes #20

README.md

@@ -3,7 +3,7 @@
 | [![Build Status](https://travis-ci.com/mateuszbaran/CovarianceEstimation.jl.svg?branch=master)](https://travis-ci.com/mateuszbaran/CovarianceEstimation.jl) [![Build status](https://ci.appveyor.com/api/projects/status/7riq3mtk8wy6k3yl?svg=true)](https://ci.appveyor.com/project/mateuszbaran/covarianceestimation-jl) | [ ![codecov.io](http://codecov.io/github/mateuszbaran/CovarianceEstimation.jl/coverage.svg?branch=master)](http://codecov.io/github/mateuszbaran/CovarianceEstimation.jl?branch=master) |
 
 # CovarianceEstimation.jl
-Lightweight covariance estimation in Julia.
+Lightweight robust covariance estimation in Julia.
 The package is currently unregistered but can be installed with `Pkg` using
 
 ```julia-repl
@@ -14,29 +14,37 @@ The package is currently unregistered but can be installed with `Pkg` using
 
 ```julia
 using CovarianceEstimation
-using Random
 
 X = randn(5, 3)
 
-S_uncorrected  = cov(Simple(), X)
-S_corrected    = cov(Corrected(), X)
-
-# using optimal shrinkage
-S_ledoitwolf   = cov(LedoitWolf(), X)
-S_rbledoitwolf = cov(RaoBlackwellLedoitWolf(), X)
-S_oracleapprox = cov(OracleApproximatingShrinkage(), X)
-
+S_uncorrected  = cov(X, Simple())
+S_corrected    = cov(X, Simple(corrected=true))
+
+# using shrinkage with different targets
+# - Ledoit-Wolf target + shrinkage
+method = LinearShrinkageEstimator(ConstantCorrelation())
+S_ledoitwolf   = cov(X, method)
+# - Chen target + shrinkage
+method = LinearShrinkageEstimator(DiagonalCommonVariance(), :rblw)
+S_chen_rblw = cov(X, method)
+method = LinearShrinkageEstimator(DiagonalCommonVariance(), :oas)
+S_chen_oas  = cov(X, method)
+
+# a pre-defined shrinkage can be used as well
+method = LinearShrinkageEstimator(DiagonalUnitVariance(), 0.5)
 # using a given shrinkage
-S_ledoitwolf_05 = cov(LedoitWolf(0.5), X)
+S_05 = cov(X, method)
 ```
 
 ## Currently supported algorithms
 
-* Basic corrected and uncorrected sample covariance (via the `Statistics` package),
-* Ledoit-Wolf shrinkage [**1**],
-* Rao-Blackwell Ledoit-Wolf shrinkage and Oracle Approximating shrinkage [**2**].
+* `Simple`: basic corrected and uncorrected sample covariance (via the `Statistics` package),
+* `LinearShrinkageEstimator`: James-Stein type estimator of the form `(1-λ)S+λF` where `S` is the uncorrected simple estimator, `F` is a target and `λ∈[0,1]` a shrinkage intensity.
+  - common targets are implemented following the taxonomy given in [**1**] along with Ledoit-Wolf optimal shrinkage intensities [**2**].
+  - in the case of the `DiagonalCommonVariance` target, a Rao-Blackwellised intensity and Oracle-Approximating intensity are also supported (see [**3**]).
 
 ## References
 
-* [**1**] O. Ledoit and M. Wolf, *[Honey, I Shrunk the Sample Covariance Matrix](http://www.ledoit.net/honey.pdf)*, The Journal of Portfolio Management, vol. 30, no. 4, pp. 110–119, Jul. 2004.
-* [**2**] Y. Chen, A. Wiesel, Y. C. Eldar, and A. O. Hero, *[Shrinkage Algorithms for MMSE Covariance Estimation](https://arxiv.org/pdf/0907.4698.pdf)*, IEEE Transactions on Signal Processing, vol. 58, no. 10, pp. 5016–5029, Oct. 2010.
+* [**1**] J. Schäfer and K. Strimmer, *[A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics](http://strimmerlab.org/publications/journals/shrinkcov2005.pdf)*, Statistical Applications in Genetics and Molecular Biology, 2005.
+* [**2**] O. Ledoit and M. Wolf, *[Honey, I Shrunk the Sample Covariance Matrix](http://www.ledoit.net/honey.pdf)*, The Journal of Portfolio Management, 2004.
+* [**3**] Y. Chen, A. Wiesel, Y. C. Eldar, and A. O. Hero, *[Shrinkage Algorithms for MMSE Covariance Estimation](https://arxiv.org/pdf/0907.4698.pdf)*, IEEE Transactions on Signal Processing, 2010.