estimate_lambda_eb: Estimate shrinkage parameter by empirical Bayes

In GabrielHoffman/mvBIC: Multivariate Information Criteria to identify important predictors in high dimensional multivariate regression

Estimate shrinkage parameter by empirical Bayes

Description

Estimate shrinkage parameter by empirical Bayes

Usage

estimate_lambda_eb(ev, n, p, nu, lambda = NULL)

Arguments

ev	array of eigen values
n	number of samples
p	number of features
nu	scale of prior covariance matrix
lambda	(default: NULL) If NULL, estimate lambda from data. Else evaluate logML using specified lambda value.

Details

Estimate shrinkage parameter for covariance matrix estimation using empirical Bayes method (Hannart and Naveau, 2014; Leday and Richardson, 2019). The shrinage estimate of the covariance matrix is (1-λ)\hatΣ + λ ν I, where \hatΣ is the sample covariance matrix, given a value of lambda. A large value of λ indicates more weight on the prior.

Value

value λ indicating the shrinkage between sample and prior covariance matrices.

Examples

ev = c(10, 2, 1) # eigen values
n = 12 # samples
p = 3 # features
nu = 2 # scale of target covariance

mvIC:::estimate_lambda_eb(ev, n, p, nu)

GabrielHoffman/mvBIC documentation built on Sept. 5, 2022, 1:57 a.m.