# alpha.crossvalid: Crossvalidation method to estimate shrinkage intensity In tpepler/cpc: Common principal component (CPC) analysis and applications

## Description

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

## Usage

 `1` ```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.

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.

`alpha.schafer`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```# 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 Nov. 19, 2017, 1:19 p.m.