alpha.crossvalid: Crossvalidation method to estimate shrinkage intensity

In tpepler/cpc: Common principal component (CPC) analysis and applications

Crossvalidation method to estimate shrinkage intensity

Description

Estimates alpha shrinkage intensity parameter by the method proposed in Pepler (2014), for improved estimation of population covariance matrices.

Usage

alpha.crossvalid(datamat, B, reps = 100)

Arguments

datamat	Matrix containing sample data for the ith group.
B	Matrix of estimated common (and possibly non-common) eigenvectors. Can be estimated using simultaneous diagonalisation algorithms such as the Flury-Gautschi (implemented in FG or the stepwise CPC (implemented in stepwisecpc) algorithms.
reps	Number of replications to use in cross-validation.

Value

Returns the estimated shrinkage intensity (scalar), a value between 0 and 1.

Author(s)

Theo Pepler

References

Pepler, P.T. (2014). The identification and application of common principal components. PhD dissertation in the Department of Statistics and Actuarial Science, Stellenbosch University.

See Also

alpha.schafer

Examples

# Versicolor and virginica groups of the Iris data
data(iris)
versicolor <- iris[51:100, 1:4]
virginica <- iris[101:150, 1:4]

# Create array containing the two covariance matrices
S <- array(NA, c(4, 4, 2))
S[, , 1] <- cov(versicolor)
S[, , 2] <- cov(virginica)
nvec <- c(nrow(versicolor), nrow(virginica))

# Estimate the modal matrix using the FG algorithm
B <- FG(covmats = S, nvec = nvec)$B

# Estimate optimal shrinkage intensity for the versicolor covariance matrix
alpha.crossvalid(datamat = versicolor, B = B, reps = 1000)

tpepler/cpc documentation built on July 7, 2022, 2:13 a.m.