ICtest (version 0.3-5)

FOBIladle: Ladle Estimate to Estimate the Number of Gaussian Components in ICA or NGCA

Description

The ladle estimator uses the eigenvalues and eigenvectors of FOBI to estimate the number of Gaussian components in ICA or NGCA.

Usage

FOBIladle(X, n.boot = 200, 
          ncomp = ifelse(ncol(X) > 10, floor(ncol(X)/log(ncol(X))), ncol(X) - 1))

Arguments

X

numeric data matrix.

n.boot

number of bootstrapping samples to be used.

ncomp

The number of components among which the ladle estimator is to be searched. The default here follows the recommendation of Luo and Li 2016.

Value

A list of class ladle containing:

method

the string FOBI.

k

the estimated number of non-gaussian components.

fn

vector giving the measures of variation of the eigenvectors using the bootstrapped eigenvectors for the different number of components.

phin

normalized eigenvalues of the FOBI matrix.

gn

the main criterion for the ladle estimate - the sum of fn and phin. k is the value where gn takes its minimum

lambda

the eigenvalues of the FOBI matrix.

W

the transformation matrix to the independent components. Also known as unmixing matrix.

S

data matrix with the centered independent components.

MU

the location of the data which was substracted before calculating the independent components.

data.name

the name of the data for which the ladle estimate was computed.

Details

The model here assumes that in ICA or NGCA there are k non-gaussian components and p-k gaussian components. The idea is then to decide which eigenvalues differ from p+2. The ladle estimate for this purpose combines the values of the scaled eigenvalues and the variation of the eigenvectors based on bootstrapping. The idea there is that for distinct eigenvales the variation of the eigenvectors is small and for equal eigenvalues the corresponding eigenvectors have large variation.

This measure is then computed assuming k=0,..., ncomp and the ladle estimate for k is the value where the measure takes its minimum.

References

Luo, W. and Li, B. (2016), Combining Eigenvalues and Variation of Eigenvectors for Order Determination, Biometrika, 103. 875--887. <doi:10.1093/biomet/asw051>

See Also

ladleplot

Examples

# NOT RUN {
n <- 1000
X <- cbind(rexp(n), rt(n,5), rnorm(n), rnorm(n), rnorm(n), rnorm(n))

test <- FOBIladle(X)
test
summary(test)
plot(test)
ladleplot(test)
# }