cov4.wt: Weighted Scatter Matrix based on Fourth Moments

In ICS: Tools for Exploring Multivariate Data via ICS/ICA

Weighted Scatter Matrix based on Fourth Moments

Description

Estimates the weighted scatter matrix based on the 4th moments of the data.

Usage

cov4.wt(x, wt = rep(1/nrow(x), nrow(x)), location = TRUE,
        method = "ML", na.action = na.fail)

Arguments

x	numeric data matrix or dataframe.
wt	numeric vector of non-negative weights. At least some weights must be larger than zero.
location	TRUE if the weighted location vector should be computed. FALSE when taken wrt to the origin. If numeric the matrix is computed wrt to the given location.
method	Either ML or unbiased. Will be passed on to cov.wt when the Mahalanobis distance is computed.
na.action	a function which indicates what should happen when the data contain 'NA's. Default is to fail.

Details

If location = TRUE, then the scatter matrix is given for a n \times p data matrix X by

\frac{1}{p+2} ave_{i}\{w_i[(x_{i}-\bar{x}_w)S_w^{-1}(x_{i}-\bar{x}_w)'](x_{i}-\bar{x}_w)'(x_{i}-\bar{x}_w)\},

where w_i are the weights standardized such that \sum{w_i}=1, \bar{x}_w is the weighted mean vector and S_w the weighted covariance matrix. For details about the weighted mean vector and weighted covariance matrix see cov.wt.

Value

A matrix containing the estimated weighted fourth moments scatter.

Author(s)

Klaus Nordhausen

See Also

cov4, cov.wt

Examples

cov.matrix.1 <- matrix(c(3,2,1,2,4,-0.5,1,-0.5,2), ncol=3)
X.1 <- rmvnorm(100, c(0,0,0), cov.matrix.1)
cov.matrix.2 <- diag(1,3)
X.2 <- rmvnorm(50, c(1,1,1), cov.matrix.2)
X <- rbind(X.1, X.2)

cov4.wt(X, rep(c(0,1), c(100,50)))
cov4.wt(X, rep(c(1,0), c(100,50)))

ICS documentation built on Sept. 21, 2023, 9:07 a.m.