nlshrink: Package

In nlshrink: Non-Linear Shrinkage Estimation of Population Eigenvalues and Covariance Matrices

Description

A package for estimating population eigenvalues and covariance matrices, based on publications by Ledoit and Wolf (2004, 2012, 2015, 2016).

Details

A common assumption in statistics is that for a data matrix X of dimension n \times p, the number of predictor variables (p) vanishes relative to the number of datapoints (n) as n \to ∞. However, in modern datasets, it is often the case that p is comparable to or greater than n. In this scenario, a more appropriate asymptotic framework is to assume that the ratio c := p/n approaches a finite positive value as n,p \to ∞. In this case, the sample covariance matrix S is no longer a consistent estimator of the population covariance matrix Σ. Similarly, the sample eigenvalues deviate substantially from the population eigenvalues. This package contains implementations of Ledoit and Wolf's linear and non-linear shrinkage population eigenvalue and covariance estimation methods, based on their 2016 publication and the accompanying MATLAB code. Theoretical and implementation details of these methods can be found in the following publications:

• Ledoit, O. and Wolf, M. (2004). A well-conditioned estimator for large-dimensional covariance matrices. Journal of Multivariate Analysis, 88(2)

• Ledoit, O. and Wolf, M. (2012). Nonlinear shrinkage estimation of large-dimensional covariance matrices. Annals of Statistics, 40(2).

• Ledoit, O. and Wolf, M. (2015). Spectrum estimation: a unified framework for covariance matrix estimation and PCA in large dimensions. Journal of Multivariate Analysis, 139(2).

• Ledoit, O. and Wolf, M. (2016). Numerical Implementation of the QuEST function. arXiv:1601.05870 [stat.CO].

nlshrink documentation built on May 1, 2019, 8:42 p.m.