casp.agg.linexloss: Coordinate-wise shrinkage prediction for aggregated targets...

In trambakbanerjee/casp: Coordinate-wise Adaptive Shrinkage Prediction

Coordinate-wise shrinkage prediction for aggregated targets under Linex loss

Description

Main function for aggregated shrinkage prediction in high-dimensional, non-exchangeable hierarchical Gaussian models with an unknown location as well as an unknown spiked covariance structure under Linex loss.

Usage

casp.agg.linexloss(X, S, A, a, tau, beta, eta, mx, mw, m0, type)

Arguments

X	a mx\times n matrix of past observations.
S	n\times n sample covariance matrix based on mw samples
A	a p\times n aggregation matrix with rank(\mathbf{A}\mathbf{A}^T)=p.
a	this is a p\times 1 vector of Linex loss parameter. See equation (4) in the casp paper.
tau	the positive scale hyper-parameter for the prior on the locations
beta	the non-negative shape hyper-parameter for the prior on the locations
eta	the prior mean of the locations
mx	the sample size of past observations \mathbf{X}
mw	the size of the side information for calculating the sample covariance matrix \mathbf{S}
m0	the sample size of the future observation. Usually this is set to 1
type	if type = 1 then all the shrinkage factors are equal to 1. If type = 0, then the shrinkage factors are estimated.

Details

This function is based on Definition 4 of the casp paper, and relies on rmt.est and Gfun.est. The shrinkage factors are estimated using the formulation given in Definition 4 and use f.agg.est in the background. Please see the casp paper in the reference for more details about these estimation techniques. If (τ,β) are unknown then one may first use taubeta.casp.est to estimate them and then use the estimated values in casp.agg.checkloss.

Value

1. q - aggregated shrinkage prediction under Linex loss for the p coordinates

2. f - estimated shrinkage factors (equal to \mathbf{1} if type = 1)

References

1. Trambak Banerjee, Gourab Mukherjee, and Debashis Paul. Improved Shrinkage Prediction under a Spiked Covariance Structure, 2021.

See Also

casp.agg.linexloss,f.agg.est,rmt.est,taubeta.casp.est

Examples

library(casp)
n = 10
p = 3
set.seed(42)
A = matrix(runif(n*p,0,1),p,n)
mx = 5
S = diag(c(10,8,6,4,rep(1,n-4)))
set.seed(42)
X<- matrix(runif(mx*n),mx,n)
tau = 1
beta = 0.5
eta = rep(0,n)
mw = 100
m0 = 1
a = rep(-1,p)
q.casp<- casp.agg.linexloss(X,S,A,a,tau,beta,eta,mx,mw,m0,0)

trambakbanerjee/casp documentation built on Nov. 22, 2022, 7:24 p.m.