# cov.trob

0th

Percentile

##### Covariance Estimation for Multivariate t Distribution

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.

Keywords
multivariate
##### Usage
cov.trob(x, wt = rep(1, n), cor = FALSE, center = TRUE, nu = 5,
maxit = 25, tol = 0.01)
##### Arguments
x
data matrix. Missing values (NAs) are not allowed.
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 = TRUE) or covariance (cor = FALSE) matrix.
center
a logical value or a numeric vector providing the location about which the covariance is to be taken. If center = FALSE, no centering is done; if center = TRUE 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
• covthe fitted covariance matrix.
• centerthe estimated or specified location vector.
• wtthe specified weights: only returned if the wt argument was given.
• n.obsthe number of cases used in the fitting.
• corthe fitted correlation matrix: only returned if cor = TRUE.
• callThe matched call.
• iterThe number of iterations used.

##### References

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.

Venables, W. N. and Ripley, B. D. (1999) Modern Applied Statistics with S-PLUS. Third Edition. Springer.

cov, cov.wt, cov.mve
cov.trob(stackloss)