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 Computation23, 441-453.