ESD: Compute the empirical spectral distribution (ESD) for a set...

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

Description

The Marcenko Pastur (MP) law relates the limiting distribution of the sample eigenvalues to that of the population eigenvalues. In the finite-dimensional case, the population spectral distribution (PSD) can be represented as a sum of point masses, and the empirical spectral distribution (ESD) can be obtained by solving the discretized MP equation. Theoretical and implementation details in the references.

Usage

ESD(tau, n)

Arguments

tau	(Required) A non-negative numeric vector of population eigenvalues.
n	(Required) A positive integer representing the number of datapoints of a hypothetical data matrix with dimension c(n, p = length(tau)).

Value

A named numeric vector of containing points of the ESD. The names give the corresponding points on the x axis.

References

• 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]

Examples

tau_ESD <- ESD(tau = rep(1,200), n = 300)
plot(names(tau_ESD), tau_ESD, ylab="F(x)", xlab="x")

Example output

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