Covariance Estimation for Multivariate t Distribution

cov.trob {MASS}

R Documentation

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 = 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

`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 = TRUE`.
`call`	The matched call.
`iter`	The 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.

Examples

cov.trob(stackloss)

[Package MASS version 7.3-51.4 Index]