| ESD {nlshrink} | R Documentation |
Compute the empirical spectral distribution (ESD) for a set of population eigenvalues
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 |
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")