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

In trambakbanerjee/casp: Coordinate-wise Adaptive Shrinkage Prediction

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

Description

Provides an estimate of the function

\mathbf{H}_{r,α,β}(\mathbf{Σ})=(\mathbf{Σ}^{-1}+τ^{-1}\mathbf{Σ}^{-β})^{-r}\mathbf{Σ}^{α}

using equation (13) of the casp paper in the reference.

Usage

hfun.est(r, alpha, beta, rmt, mx, tau)

Arguments

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
rmt	the output from rmt.est
mx	the sample size of the past observations \mathbf{X}
tau	the positive scale hyper-parameter for the prior on the locations

Details

This function relies on the output from rmt.est and is called by casp.checkloss, casp.linexloss and their counterparts for aggregated prediction. Please see equation (13) of the casp paper in the reference to get more details about the estimation.

Value

1. h - an estimate of H_{r,α,β}(\mathbf{Σ})

References

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

See Also

rmt.est, casp.checkloss, casp.linexloss

Examples

library(casp)
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)
H.hat<- hfun.est(r,alpha,beta,rmt,mx,tau)

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