Covariance Estimation for Multivariate t Distribution

DESCRIPTION:

Estimates a covariance or correlation matrix assuming the data came from a multivariate t distribution: this provides some degree of robustness to outlier without giving a high breakdown point.

USAGE:

cov.trob(x, wt = rep(1, n), cor = F, center = T, nu = 5, maxit = 25,
         tol = 0.01)

REQUIRED ARGUMENTS:

x
data matrix. Missing values (NAs) are not allowed.

OPTIONAL ARGUMENTS:

wt
A vector of weights for each case: these are treated as if the case i actually occurred wt[i] times.
cor
Flag to choose between returning the correlation ( cor=T) or covariance ( cor=F) matrix.
center
a logical value or a numeric vector providing the location about which the covariance is to be taken. If center = F, no centering is done; if center = T the MLE of the location vector is used.
nu
degrees of freedom for the multivariate t distribution. Must exceed 2 (so that the covariance matrix is finite).
maxit
Maximum number of iterations in fitting.
tol
Convergence tolerance for fitting.

VALUE:

A list with the following components
cov
the fitted covariance matrix.
center
the estimated or specified location vector.
wt
the specified weights: only returned if the wt argument was given.
n.obs
the number of cases used in the fitting.
cor
the fitted correlation matrix: only returned if cor = T.
call
The matched call.
iter
The number of iterations used.

REFERENCE:

J. T. Kent, D. E. Tyler and Y. Vardi (1994) A curious likelihood identity for the multivariate t-distribution. Communications in Statistics---Simulation and Computation 23, 441-453.

SEE ALSO:

, ,

EXAMPLES:

stackloss <- data.frame(stack.x, stack.loss)
cov.trob(stackloss)