cov4.wt: Weighted Scatter Matrix based on Fourth Moments In ICS: Tools for Exploring Multivariate Data via ICS/ICA

Description

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

Usage

 ```1 2``` ```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 x p data matrix X by

1/(p+2) ave{w_i[(x_i-x_bar)S^{-1}(x_i-x_bar)'] (x_i-x_bar)'(x_i-x_bar)},

where w_i are the weights standardized such that sum(w_i)=1, x_bar is the weighted mean vector and S the weighted covariance matrix. For details about the weighted mean vector and weighted covariance matrix see `cov.wt`.

A matrix.

Author(s)

Klaus Nordhausen

`cov4`, `cov.wt`
 ```1 2 3 4 5 6 7 8``` ```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))) ```