Gfun.est: Provides an estimate of the function...

In trambakbanerjee/casp: Coordinate-wise Adaptive Shrinkage Prediction

Provides an estimate of the function \mathbf{G}_{r,α,β}(\mathbf{Σ},\mathbf{A})

Description

Provides an estimate of the function \mathbf{G}_{r,α,β}(\mathbf{Σ},\mathbf{A}) using the display in Section 4 of the casp paper in the reference.

Usage

Gfun.est(A, r, alpha, beta, tau, rmt, mx)

Arguments

A	a p\times n aggregation matrix with rank(\mathbf{A}\mathbf{A}^T)=p
r	a value in \{-1,0,1\}
alpha	a non-negative number
beta	the non-negative shape hyper-parameter for the prior on the locations
tau	the positive scale hyper-parameter for the prior on the locations
rmt	the output from rmt.est
mx	the sample size of the past observations \mathbf{X}

Details

This function relies on the output from rmt.est and is called by casp.agg.checkloss, and casp.agg.linexloss. Please see Section 4 of the casp paper in the reference to get more details about the estimation.

Value

1. Gfun - an estimate of G_{r,α,β}(\mathbf{Σ},\mathbf{A})

References

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

See Also

rmt.est, casp.agg.checkloss, casp.agg.linexloss

Examples

library(casp)
n = 10
p = 3
set.seed(42)
A = matrix(runif(n*p,0,1),p,n)
r = 1
alpha = 0
tau = 1
beta = 0.5
mx = 1
K = 4
S = diag(c(10,8,6,4,rep(1,6)))
mw = 50
rmt<- rmt.est(K,S,mw)
Gfun.out<- Gfun.est(A,r,alpha,beta,tau,rmt,mx)

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