ICS (version 1.4-1)

mean3: Location Estimate based on Third Moments

Description

Estimates the location based on third moments.

Usage

mean3(X, na.action = na.fail)

Value

A vector.

Arguments

X

numeric data matrix or dataframe with at least two columns.

na.action

a function which indicates what should happen when the data contain 'NA's. Default is to fail.

Author

Klaus Nordhausen

Details

This location estimate is defined for a \(n \times p\) matrix X as $$ \frac{1}{p} ave_{i}\{[(x_{i}-\bar{x})S^{-1}(x_{i}-\bar{x})'] x_{i}\},$$ where \(\bar{x}\) is the mean vector and \(S\) the regular covariance matrix.

References

Oja, H., Sirki?, S. and Eriksson, J. (2006), Scatter matrices and independent component analysis, Austrian Journal of Statistics, 35, 175--189.

Examples

set.seed(654321)
cov.matrix <- matrix(c(3,2,1,2,4,-0.5,1,-0.5,2), ncol=3)
X <- rmvnorm(100, c(0,0,0), cov.matrix)
mean3(X)
rm(.Random.seed)